Question

Simplify $\frac{1}{1-z}$, given $z = \cos \vartheta+ i\sin \vartheta$

score 80 · Answer 1 · 2026-04-12 16:26:08

80

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Simplify $\frac{1}{1-z}$, given $z = \cos \vartheta+ i\sin \vartheta$

Published on 12 Apr 2026 - 16:26

score 388 · Answer 2 · 2026-03-28 15:19:53

388

Views

linear least squares -- complex observations, real estimate constraint

Published on 28 Mar 2026 - 15:19

score 266 · Answer 3 · 2026-04-13 19:11:33

266

Views

Find locus of $S$ denoting set of complex numbers $\frac{z+1}{z-3}$, where $z$ varies over set of $|z|=1$.

Published on 13 Apr 2026 - 19:11

score 202 · Answer 4 · 2026-04-16 14:57:10

202

Views

Describing and sketching a set of complex numbers satisfying certain conditions

Published on 16 Apr 2026 - 14:57

score 119 · Answer 5 · 2026-04-10 02:36:07

119

Views

Modulus of complex root

Published on 10 Apr 2026 - 2:36

score 1.2k · Answer 6 · 2026-04-14 13:11:00

1.2k

Views

Describing and sketching the set of complex numbers satisfying certain conditions

Published on 14 Apr 2026 - 13:11

score 171 · Answer 7 · 2026-04-13 00:13:50

171

Views

Summation of complex roots

Published on 13 Apr 2026 - 0:13

score 124 · Answer 8 · 2026-04-14 16:32:21

124

Views

Let $f(X)$ be a compl. quadr. with real roots 1/3 and 2/3 If $|z| = 1$, what is the sum of all possible values of $f(z)$ such that $f(z) = f(z)$?

Published on 14 Apr 2026 - 16:32

score 45 · Answer 9 · 2026-04-14 07:54:15

45

Views

Uniqueness of Laurent Series in $|z| = 1$

Published on 14 Apr 2026 - 7:54

score 118 · Answer 10 · 2026-04-12 01:31:41

118

Views

Determining arg of a complex number in Euler form

Published on 12 Apr 2026 - 1:31

score 48 · Answer 11 · 2026-04-16 07:21:38

48

Views

Solving $z^3=1, z \in \mathbb{C}$

Published on 16 Apr 2026 - 7:21

score 144 · Answer 12 · 2026-04-15 08:47:14

144

Views

Prove $\|x\|+\|y\|+\|z\|+\|x+y+z\| \ge \|x+y\|+\|y+z\|+\|z+x\|$

Published on 15 Apr 2026 - 8:47

score 524 · Answer 13 · 2026-04-16 01:26:43

524

Views

Using roots of unity to prove that $\cos\frac{\pi}{2n}\cos\frac{2\pi}{2n}\cdots\cos\frac{(n-1)\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}}$

Published on 16 Apr 2026 - 1:26

score 1.5k · Answer 14 · 2026-03-26 06:31:51

1.5k

Views

A variable parabola touches the $x$-axis and $y$-axis at $A(1,0)$ and $B(0,1)$. Find the locus of its focus.

Published on 26 Mar 2026 - 6:31

score 54 · Answer 15 · 2026-04-09 09:10:30

54

Views

Converting from complex fourier series to real

Published on 09 Apr 2026 - 9:10

List Question

Simplify $\frac{1}{1-z}$, given $z = \cos \vartheta+ i\sin \vartheta$

linear least squares -- complex observations, real estimate constraint

Find locus of $S$ denoting set of complex numbers $\frac{z+1}{z-3}$, where $z$ varies over set of $|z|=1$.

Describing and sketching a set of complex numbers satisfying certain conditions

Modulus of complex root

Describing and sketching the set of complex numbers satisfying certain conditions

Summation of complex roots

Let $f(X)$ be a compl. quadr. with real roots 1/3 and 2/3 If $|z| = 1$, what is the sum of all possible values of $f(z)$ such that $f(z) = f(z)$?

Uniqueness of Laurent Series in $|z| = 1$

Determining arg of a complex number in Euler form

Solving $z^3=1, z \in \mathbb{C}$

Prove $\|x\|+\|y\|+\|z\|+\|x+y+z\| \ge \|x+y\|+\|y+z\|+\|z+x\|$

Using roots of unity to prove that $\cos\frac{\pi}{2n}\cos\frac{2\pi}{2n}\cdots\cos\frac{(n-1)\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}}$

A variable parabola touches the $x$-axis and $y$-axis at $A(1,0)$ and $B(0,1)$. Find the locus of its focus.

Converting from complex fourier series to real

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