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Tag
complex
Recent questions tagged complex
30
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1
answers
What is the significance of complex integration along a contour?
What is the significance of complex integration along a contour?
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Apr 8
Mathematics
significance
complex
integration
contour
+
–
37
views
1
answers
Define a complex number and its basic properties.
Define a complex number and its basic properties.
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113k
points
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asked
Apr 8
Mathematics
define
complex
number
basic
properties
+
–
63
views
1
answers
What is the conjugate of the complex number \(7+3i\) ?
What is the conjugate of the complex number \(7+3i\) ?
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113k
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asked
Mar 25
Mathematics
complex
real
equation
function
imaginary
conjugate
number
+
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124
views
1
answers
Suppose $f, g$ are entire functions, and suppose that for all $z \in \mathbb{C}$, that $| f(z) | \leq | g(z)|$. What conclusion can you draw?
Suppose $f, g$ are entire functions, and suppose that for all $z \in \mathbb{C}$, that $| f(z) | \leq | g(z)|$. What conclusion can you draw?
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113k
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Mar 10
Mathematics
function
real
numbers
complex
formula
approximation
estimate
+
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71
views
1
answers
explain the product of two complex numbers using their conjugated
explain why $z1 \times z2 = (\bar{z1}\times z2 + z1 \times \bar{z2})/2
anonymous
anonymous
asked
Jan 12
Mathematics
complex
product
solutions
+
–
139
views
1
answers
Simplify the complex expression \[ (2-3 i)(-2+i) \]
Simplify the complex expression\[(2-3 i)(-2+i)\]
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113k
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asked
Aug 3, 2023
Mathematics
number
expression
complex
simplify
imaginary
real
bnu-1501
+
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128
views
1
answers
Simplify the complex number \(5(3-2 i)+2 i(4+6 i)\)
Simplify the complex number \(5(3-2 i)+2 i(4+6 i)\)
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Platinum
113k
points
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asked
Aug 3, 2023
Mathematics
number
complex
simplify
imaginary
real
bnu-1501
expression
+
–
343
views
1
answers
Which expression is equivalent to \(9 x^2-16 y^2 ?\)
Which expression is equivalent to \(9 x^2-16 y^2 ?\)
Edzai Zvobwo
Bronze Status
6.2k
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Edzai Zvobwo
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Jul 16, 2023
Mathematics
function
numbers
calculate
complex
jee
approximation
formula
+
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167
views
1
answers
(Lael and Nourouzi 2008) Let \((V, \mu, \nu)\) be an \(I F\)-normed space. Assume further that \(\mu(x, t)>0\) for all \(t>0\) implies \(x=0\).
(Lael and Nourouzi 2008) Let \((V, \mu, \nu)\) be an \(I F\)-normed space. Assume further that \(\mu(x, t)>0\) for all \(t>0\) implies \(x=0\). Define\[\|x\|_\alpha=\inf ...
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113k
points
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asked
May 21, 2023
Mathematics
real
set
complex
jee
numbers
associative
law
+
–
318
views
1
answers
Give an example of how to find the roots of a complex number.
Give an example of how to find the roots of a complex number. use latex
MathsGee
Platinum
113k
points
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asked
Mar 29, 2023
Mathematics
example
roots
complex
number
+
–
485
views
1
answers
What is a complex root?
What is a complex root? use latex
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Platinum
113k
points
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asked
Mar 29, 2023
Mathematics
complex
equation
root
number
+
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327
views
1
answers
What are the basic operations of complex numbers?
What are the basic operations of complex numbers? Use latex and give examples for each.
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Platinum
113k
points
MathsGee
asked
Mar 29, 2023
Mathematics
numbers
complex
imaginary
argand
real
solution
+
–
657
views
1
answers
Explain the polar form of complex numbers with an example and use latex
Explain the polar form of complex numbers with an example and use latex
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Platinum
113k
points
MathsGee
asked
Mar 29, 2023
Mathematics
explain
polar
form
complex
numbers
latex
+
–
488
views
2
answers
What happens when you multiply a complex number by its conjugate?
What happens when you multiply a complex number by its conjugate? Give an example and use latex
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Platinum
113k
points
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asked
Mar 29, 2023
Mathematics
complex
real
function
equation
+
–
511
views
1
answers
Give 10 examples of complex conjugate pairs.
Give 10 examples of complex conjugate pairs. use latex
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Platinum
113k
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asked
Mar 29, 2023
Mathematics
examples
complex
conjugate
pairs
+
–
390
views
1
answers
What is conjugation in complex numbers?
What is conjugation in complex numbers? use latex
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Platinum
113k
points
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asked
Mar 29, 2023
Mathematics
complex
numbers
imaginary
argand
solution
+
–
479
views
1
answers
WHat are complex numbers?
WHat are complex numbers? use latex
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Platinum
113k
points
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asked
Mar 29, 2023
Mathematics
complex
numbers
imaginary
argand
+
–
1.6k
views
1
answers
The inverse of \(-i\) in the multiplicative group, \(1,-1, i,-i\) is
The inverse of \(-i\) in the multiplicative group, \(1,-1, i,-i\) is
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Platinum
113k
points
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asked
Mar 15, 2023
Mathematics
inverse
multiplicative
complex
imaginary
numbers
+
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768
views
2
answers
What is a zero-matrix?
What is a zero-matrix?
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9.4k
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Mar 7, 2023
Mathematics
zero-matrix
matrix
real
eigenvalue
square
complex
invertible
+
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463
views
1
answers
Multiply \(3+\mathrm{i} \sqrt{3}\) by its complex conjugate.
Multiply \(3+\mathrm{i} \sqrt{3}\) by its complex conjugate.
Maths-Genie
Bronze Status
9.4k
points
Maths-Genie
asked
Feb 20, 2023
Mathematics
complex
imaginary
solution
real
function
equation
point
+
–
219
views
1
answers
For \(\mathrm{i}=\sqrt{-1}\), what is the result of subtracting \((2+4 \mathrm{i})\) from \((-5+6 \mathrm{i}) ?\)
For \(\mathrm{i}=\sqrt{-1}\), what is the result of subtracting \((2+4 \mathrm{i})\) from \((-5+6 \mathrm{i}) ?\)
Maths-Genie
Bronze Status
9.4k
points
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Feb 20, 2023
Mathematics
complex
numbers
imaginary
+
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718
views
1
answers
What is a CCP Complex?
What is a CCP Complex?
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9.4k
points
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Feb 13, 2023
General Knowledge
ccp
complex
serum
+
–
319
views
1
answers
What is a complex number?
What is a complex number?
AstraNova
Diamond
67.9k
points
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Jan 27, 2023
Mathematics
complex
numbers
real
imaginary
number
identify
+
–
279
views
1
answers
What is the formula for the area of a parallelogram?
What is the formula for the area of a parallelogram?
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 27, 2023
Mathematics
area
parallelogram
unit
convex
polygon
vertices
complex
+
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648
views
1
answers
Prove that the roots of a polynomial with real coefficients are either real or come in conjugate pairs.
Prove that the roots of a polynomial with real coefficients are either real or come in conjugate pairs.
AstraNova
Diamond
67.9k
points
AstraNova
asked
Jan 27, 2023
Mathematics
polynomial
coefficients
cubic
graph
real
numbers
complex
+
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336
views
0
answers
If \(x\) is a real number such that \((x-3)(x-1)(x+1)(x+3)+16=116^2\), what is the largest possible value of \(x\) ?
If \(x\) is a real number such that \((x-3)(x-1)(x+1)(x+3)+16=116^2\), what is the largest possible value of \(x\) ?
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113k
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Dec 8, 2022
Mathematics
real
numbers
jee
set
integers
complex
associative
+
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385
views
0
answers
How many quadratics are there with these properties?
Mr. Jones teaches algebra. He has a whiteboard with a pre-drawn coordinate grid that runs from \(-10\) to 10 in both the \(x\) and \(y\) coordinates. Consequently, when h...
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Platinum
113k
points
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asked
Dec 8, 2022
Mathematics
numbers
combinations
permutations
set
integers
real
complex
+
–
361
views
0
answers
How many cool sequences are there?
Say that a sequence \(a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8\) is cool if- the sequence contains each of the integers 1 through 8 exactly once, and- every pair of consecu...
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Dec 8, 2022
Mathematics
combinations
permutations
numbers
integers
set
real
complex
+
–
394
views
0
answers
Let \(H\) be a regular hexagon with area 360 . Three distinct vertices \(X, Y\), and \(Z\) are picked randomly, with all possible triples of distinct vertices equally likely. Let \(A, B\), and \(C\) be the unpicked vertices.
Let \(H\) be a regular hexagon with area 360 . Three distinct vertices \(X, Y\), and \(Z\) are picked randomly, with all possible triples of distinct vertices equally lik...
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Platinum
113k
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MathsGee
asked
Dec 8, 2022
Mathematics
real
numbers
set
jee
integers
complex
associative
+
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202
views
0
answers
The roots of the polynomial \(x^4-4 i x^3+3 x^2-14 i x-44\) form the vertices of a parallelogram in the complex plane. What is the area of the parallelogram?
The roots of the polynomial \(x^4-4 i x^3+3 x^2-14 i x-44\) form the vertices of a parallelogram in the complex plane. What is the area of the parallelogram?
MathsGee
Platinum
113k
points
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asked
Dec 8, 2022
Mathematics
roots
polynomial
vertices
complex
plane
+
–
196
views
0
answers
The imaginary part of \((3+2 \sqrt{-54})^{\frac{1}{2}}-(3-2 \sqrt{-54})^{\frac{1}{2}}\) can be
The imaginary part of \((3+2 \sqrt{-54})^{\frac{1}{2}}-(3-2 \sqrt{-54})^{\frac{1}{2}}\) can be(1) \(\sqrt{-6}\)(2) \(\sqrt{6}\)(3) \(-2 \sqrt{6}\)(4) 6
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Nov 29, 2022
Mathematics
numbers
complex
imaginary
positive
integers
prime
part
+
–
511
views
1
answers
We have a chessboard of size \(\left(k^2-k+1\right) \times\left(k^2-k+1\right)\), where \(k-1=p\) is a prime number.
We have a chessboard of size \(\left(k^2-k+1\right) \times\left(k^2-k+1\right)\), where \(k-1=p\) is a prime number. For each prime \(p\), give a method of distribution o...
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113k
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asked
Sep 23, 2022
Mathematics
set
real
jee
numbers
complex
integers
nominal
+
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247
views
0
answers
The positive integers \(a, b, c, d, p\), and \(q\) satisfy \(a d-b c=1\) and \(\frac{a}{b}>\frac{p}{q}>\frac{c}{d}\). Prove that:
The positive integers \(a, b, c, d, p\), and \(q\) satisfy \(a d-b c=1\) and \(\frac{a}{b}>\frac{p}{q}>\frac{c}{d}\). Prove that: (a) \(q \geq b+d\);(b) If \(q=b+d\), the...
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113k
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asked
Sep 23, 2022
Mathematics
set
real
numbers
jee
integers
complex
associative
+
–
558
views
0
answers
Let \(x \leq y \leq z\) be real numbers such that \(x y+y z+z x=1\). Prove that \(x z<\frac{1}{2}\). Is it possible to improve the value of constant \(\frac{1}{2}\) ?
Let \(x \leq y \leq z\) be real numbers such that \(x y+y z+z x=1\). Prove that \(x z<\frac{1}{2}\). Is it possible to improve the value of constant \(\frac{1}{2}\) ?
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113k
points
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asked
Sep 23, 2022
Mathematics
real
set
numbers
jee
complex
associative
integers
+
–
416
views
1
answers
Let \(z_1, z_2, z_3\) be pairwise distinct complex numbers satisfying \(\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=\) 1 and
Let \(z_1, z_2, z_3\) be pairwise distinct complex numbers satisfying \(\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=\) 1 and\[\frac{1}{2+\left|z_1+z_2\right|}+\fra...
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Platinum
113k
points
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asked
Sep 23, 2022
Mathematics
numbers
complex
matrices
vectors
solution
imaginary
argand
+
–
362
views
0
answers
If \(a, b, c\) are nonnegative real numbers with \(a^2+b^2+c^2=1\), prove that
If \(a, b, c\) are nonnegative real numbers with \(a^2+b^2+c^2=1\), prove that\[\frac{a}{b^2+1}+\frac{b}{c^2+1}+\frac{c}{a^2+1} \geq \frac{3}{4}(a \sqrt{a}+b \sqrt{b}+c \...
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113k
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asked
Sep 23, 2022
Mathematics
real
numbers
set
jee
integers
complex
associative
+
–
554
views
0
answers
For any set \(A\) of positive integers, let \(n_A\) be the number of triples \((x, y, z)\) of elements of \(A\) with \(x<y\) and \(x+y=z\). If \(A\) is a seven-element set, find the maximum possible value of \(n_A\).
For any set \(A\) of positive integers, let \(n_A\) be the number of triples \((x, y, z)\) of elements of \(A\) with \(x<y\) and \(x+y=z\). If \(A\) is a seven-element se...
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113k
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asked
Sep 22, 2022
Mathematics
numbers
real
set
integers
complex
jee
associative
+
–
437
views
0
answers
Messages are coded as sequences of zeros and ones. Only sequences with not more than two consecutive zeros or ones are allowed. How many permitted 12digit sequences are there?
Messages are coded as sequences of zeros and ones. Only sequences with not more than two consecutive zeros or ones are allowed. How many permitted 12digit sequences are t...
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Platinum
113k
points
MathsGee
asked
Sep 22, 2022
Mathematics
combinations
permutations
numbers
integers
set
real
complex
+
–
234
views
0
answers
Let \(T(n)\) be the sum of the decimal digits of a natural number \(n\).
Let \(T(n)\) be the sum of the decimal digits of a natural number \(n\). (a) Find a natural number \(N\) such that \(T(k N)\) is even for all \(k=1,2, \ldots, 1992\), but...
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Platinum
113k
points
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asked
Sep 22, 2022
Mathematics
numbers
real
set
integers
jee
complex
associative
+
–
219
views
0
answers
Let \(s(t)\) denote the number of digits of a natural number \(t\). Find all solutions to the system
Let \(s(t)\) denote the number of digits of a natural number \(t\). Find all solutions to the system\[\begin{aligned}s(x)+s(y) &=x \\x+y+s(z) &=z \\s(x)+s(y)+s(z) &=y-4\e...
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Platinum
113k
points
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asked
Sep 22, 2022
Mathematics
real
numbers
set
integers
complex
jee
associative
+
–
229
views
0
answers
Let \(a, b\) and \(c\) be positive real numbers. Prove that \[ \frac{a}{b}+\frac{b}{c}+\frac{c}{a} \leq \frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2} . \]
Let \(a, b\) and \(c\) be positive real numbers. Prove that\[\frac{a}{b}+\frac{b}{c}+\frac{c}{a} \leq \frac{a^2}{b^2}+\frac{b^2}{c^2}+\frac{c^2}{a^2} .\]
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Sep 22, 2022
Mathematics
real
numbers
set
jee
integers
complex
associative
+
–
229
views
1
answers
If \(a, b, c\) are positive real numbers that satisfy \[ \frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}=1 \] prove that \(|a b c| \leq \frac{1}{2 \sqrt{2}}\)
If \(a, b, c\) are positive real numbers that satisfy\[\frac{a^2}{1+a^2}+\frac{b^2}{1+b^2}+\frac{c^2}{1+c^2}=1\]prove that \(|a b c| \leq \frac{1}{2 \sqrt{2}}\)
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113k
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asked
Sep 22, 2022
Mathematics
real
numbers
jee
integers
set
complex
associative
+
–
195
views
1
answers
If \(a, b, c\) are positive real numbers that satisfy \(a^2+b^2+c^2=1\), find the minimal value of
If \(a, b, c\) are positive real numbers that satisfy \(a^2+b^2+c^2=1\), find the minimal value of\[S=\frac{a^2 b^2}{c^2}+\frac{b^2 c^2}{a^2}+\frac{c^2 a^2}{b^2}\]
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113k
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asked
Sep 22, 2022
Mathematics
numbers
jee
real
integers
complex
set
associative
+
–
272
views
0
answers
Given that \(z=3-3 \mathrm{i}\) express, in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are real numbers,
Given that \(z=3-3 \mathrm{i}\) express, in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are real numbers,(a) \(z^2\),(b) \(\frac{1}{z}\).(c) Find the exact value o...
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113k
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asked
Sep 13, 2022
Mathematics
complex
form
numbers
equations
system
linear
solve
+
–
250
views
0
answers
Find \(\frac{\mathrm{z}_2}{\mathrm{z}_1}\) in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are expressed in terms of \(p\).
The complex numbers \(z_1\) and \(z_2\) are given by\[\begin{aligned}&z_1=5+3 \mathrm{i} \\&z_2=1+p \mathrm{i}\end{aligned}\]where \(p\) is an integer.(a) Find \(\frac{\m...
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113k
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asked
Sep 13, 2022
Mathematics
form
numbers
complex
solve
equations
linear
system
+
–
512
views
0
answers
Find the roots of the equation \[ z^2+2 z+17=0, \]
(a) Find the roots of the equation\[z^2+2 z+17=0,\]giving your answers in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are integers.(b) Show these roots on an Argan...
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113k
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asked
Sep 13, 2022
Mathematics
complex
equation
solution
numbers
real
jee
roots
+
–
319
views
1
answers
\[ z=\sqrt{3}-\mathrm{i} . \] \(\mathrm{z}^*\) is the complex conjugate of \(\mathrm{z}\). (a) Show that \(\frac{z}{z^*}=\frac{1}{2}-\frac{\sqrt{3}}{2} i\).
\[z=\sqrt{3}-\mathrm{i} .\]\(\mathrm{z}^*\) is the complex conjugate of \(\mathrm{z}\).(a) Show that \(\frac{z}{z^*}=\frac{1}{2}-\frac{\sqrt{3}}{2} i\).(b) Find the value...
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113k
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Sep 13, 2022
Mathematics
complex
real
imaginary
solution
function
equation
point
+
–
187
views
0
answers
The complex number \(z\) is defined by
The complex number \(z\) is defined by\[z=\frac{a+2 \mathrm{i}}{a-\mathrm{i}}, a \in \Re, a>0\]Given that the real part of \(z\) is \(\frac{1}{2}\), find(a) the value of ...
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113k
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Sep 13, 2022
Mathematics
complex
function
derivative
schwarzian
analysis
holomorphic
numbers
+
–
287
views
1
answers
The complex numbers \(z_1\) and \(z_2\) are given by \[ z_1=2-\mathrm{i} \text { and } z_2=-8+9 \mathrm{i} \]
The complex numbers \(z_1\) and \(z_2\) are given by\[z_1=2-\mathrm{i} \text { and } z_2=-8+9 \mathrm{i}\](a) Show \(z_1\) and \(z_2\) on a single Argand diagram.Find, sh...
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Platinum
113k
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asked
Sep 13, 2022
Mathematics
numbers
solution
complex
argand
imaginary
matrices
vectors
+
–
788
views
1
answers
The complex numbers \(z_1\) and \(z_2\) are given by \[ z_1=2+8 \mathrm{i} \text { and } z_2=1-\mathrm{i} \]
The complex numbers \(z_1\) and \(z_2\) are given by\[z_1=2+8 \mathrm{i} \text { and } z_2=1-\mathrm{i}\]Find, showing your working,(a) \(\frac{z_1}{z_2}\) in the form \(...
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113k
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Sep 13, 2022
Mathematics
numbers
complex
solution
imaginary
argand
matrices
vectors
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