Question

All solutions of $\frac{n}{2z} = \sum\limits_{i=1}^n \frac{1}{z-c_i}$ lie on the unit circle given that $|c_i| = 1, 1 \le i \le n.$

score 59 · Answer 1 · 2026-04-16 05:29:42

59

Views

All solutions of $\frac{n}{2z} = \sum\limits_{i=1}^n \frac{1}{z-c_i}$ lie on the unit circle given that $|c_i| = 1, 1 \le i \le n.$

Published on 16 Apr 2026 - 5:29

score 62 · Answer 2 · 2026-03-26 04:32:19

62

Views

Geometric Interpretation of a question related to complex numbers..

Published on 26 Mar 2026 - 4:32

score 189 · Answer 3 · 2026-04-17 06:20:58

Evaluate $|z_1 + z_2 + z_3|$ on unit circle given $ \frac{ z_1^2}{z_2 z_3} + \frac{ z_2^2}{z_1 z_3} + \frac{ z_3^2}{z_1 z_2} +1 =0$

score 463 · Answer 4 · 2026-04-15 19:52:31

463

Views

Are the singularities of $f(z) = \frac{z^2+1}{z^2(z+1)}$ removable?

Published on 15 Apr 2026 - 19:52

score 82 · Answer 5 · 2026-04-16 07:40:01

82

Views

Find the singularities of $f(z) =\frac{1}{(2\sin z - 1)^2}$.

Published on 16 Apr 2026 - 7:40

score 985 · Answer 6 · 2026-04-13 13:21:42

985

Views

Prove that if the only singularities of a function are poles then the function must be rational.

Published on 13 Apr 2026 - 13:21

score 58 · Answer 7 · 2026-04-17 04:45:41

58

Views

Solve for $x$, $(1+2i)^{(2x+6)}=(-11-2i)^{(x+1)} $

Published on 17 Apr 2026 - 4:45

score 67 · Answer 8 · 2026-04-16 01:47:06

67

Views

Map complex shape onto $w=iz^2$

Published on 16 Apr 2026 - 1:47

score 206 · Answer 9 · 2026-04-17 15:56:42

206

Views

$\prod_{k=1}^{m}\sin(kt)$ related identity

Published on 17 Apr 2026 - 15:56

score 261 · Answer 10 · 2026-04-15 13:34:49

261

Views

Solving $\cos(z) = \frac{5}{2}$

Published on 15 Apr 2026 - 13:34

score 111 · Answer 11 · 2026-04-16 22:51:38

111

Views

Find all $z$ such that $|\cos z|^2+|\sin z|^2=4$

Published on 16 Apr 2026 - 22:51

score 36 · Answer 12 · 2026-04-17 06:24:36

36

Views

Find a geometric description of $y=y_0$ under the mapping $w=1/z$

Published on 17 Apr 2026 - 6:24

score 49 · Answer 13 · 2026-05-15 12:46:28

49

Views

Find $w^2$ and compute a quadratic equation satisfied by $w$

Published on 15 May 2026 - 12:46

score 223 · Answer 14 · 2026-05-16 01:07:36

223

Views

If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

Published on 16 May 2026 - 1:07

score 710 · Answer 15 · 2026-04-13 23:08:01

710

Views

If $zw$ is real, must $w$ be a multiple of the conjugate of $z$?

Published on 13 Apr 2026 - 23:08

List Question

All solutions of $\frac{n}{2z} = \sum\limits_{i=1}^n \frac{1}{z-c_i}$ lie on the unit circle given that $|c_i| = 1, 1 \le i \le n.$

Geometric Interpretation of a question related to complex numbers..

Evaluate $|z_1 + z_2 + z_3|$ on unit circle given $ \frac{ z_1^2}{z_2 z_3} + \frac{ z_2^2}{z_1 z_3} + \frac{ z_3^2}{z_1 z_2} +1 =0$

Are the singularities of $f(z) = \frac{z^2+1}{z^2(z+1)}$ removable?

Find the singularities of $f(z) =\frac{1}{(2\sin z - 1)^2}$.

Prove that if the only singularities of a function are poles then the function must be rational.

Solve for $x$, $(1+2i)^{(2x+6)}=(-11-2i)^{(x+1)} $

Map complex shape onto $w=iz^2$

$\prod_{k=1}^{m}\sin(kt)$ related identity

Solving $\cos(z) = \frac{5}{2}$

Find all $z$ such that $|\cos z|^2+|\sin z|^2=4$

Find a geometric description of $y=y_0$ under the mapping $w=1/z$

Find $w^2$ and compute a quadratic equation satisfied by $w$

If $a_i\in\mathbb{R}$, $\omega^2+\omega+1=0$, and $\sum_{i=1}^n\frac{1}{a_i+\omega^k} =2\omega^{2k}$ for $k=1,2$, find $\sum_{i=1}^n\frac{1}{a_i+1}$.

If $zw$ is real, must $w$ be a multiple of the conjugate of $z$?

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