Question

If $|z| = 1, z \in \mathbb{C}$, what can you say about the real and imaginary parts of $z^i$

score 54 · Answer 1 · 2026-04-14 21:36:28

54

Views

If $|z| = 1, z \in \mathbb{C}$, what can you say about the real and imaginary parts of $z^i$

Published on 14 Apr 2026 - 21:36

score 117 · Answer 2 · 2026-03-25 06:12:21

117

Views

Am I combining Cauchy and Taylor theorems to prove this Taylor representation correctly?

Published on 25 Mar 2026 - 6:12

score 82 · Answer 3 · 2026-04-12 22:29:17

82

Views

Unique Representation of Elements in the Complex Circle Group

Published on 12 Apr 2026 - 22:29

score 1.2k · Answer 4 · 2026-03-25 06:12:57

1.2k

Views

Integrating $\int_{C(0,1)} \frac{1}{(z-a)(z-b)}dz$ for various cases of a and b being/not being in C

Published on 25 Mar 2026 - 6:12

score 306 · Answer 5 · 2026-04-14 11:31:09

306

Views

Montel's theorem to show normal family

Published on 14 Apr 2026 - 11:31

score 1.3k · Answer 6 · 2026-04-15 16:37:44

1.3k

Views

Prove the radius of convergence of the complex power series $(z^2 - 1)/(z^3-1)$ about $z =2$ is sqrt(7)

Published on 15 Apr 2026 - 16:37

score 134 · Answer 7 · 2026-04-15 07:48:44

134

Views

Is the integral $\int_{-\infty}^{\infty}\frac{\sin(x)}{x^2}dx$ equal to zero?

Published on 15 Apr 2026 - 7:48

score 115 · Answer 8 · 2026-04-23 03:01:26

115

Views

Give the largest open set where the function $f(z)=\sum_{n=1}^{\infty} ne^{nz}$

Published on 23 Apr 2026 - 3:01

score 464 · Answer 9 · 2026-04-11 17:28:40

464

Views

A nonvanishing entire function of finite order is the logarithm of a polynomial

Published on 11 Apr 2026 - 17:28

score 314 · Answer 10 · 2026-04-16 04:40:59

314

Views

To Prove that $\ f(z)=cz^n$

Published on 16 Apr 2026 - 4:40

score 114 · Answer 11 · 2026-04-13 10:18:56

114

Views

Donald Sarason's problem X.20.3

Published on 13 Apr 2026 - 10:18

score 794 · Answer 12 · 2026-04-16 05:42:38

794

Views

Is it always true that $Log(z^{-1})=-Log(z)$

Published on 16 Apr 2026 - 5:42

score 318 · Answer 13 · 2026-04-10 19:08:59

318

Views

An expression for sin(40)

Published on 10 Apr 2026 - 19:08

score 58 · Answer 14 · 2026-04-13 09:08:16

58

Views

Show that a sequence having a finite limit point cannot approach \infty

Published on 13 Apr 2026 - 9:08

score 287 · Answer 15 · 2026-04-13 19:37:41

287

Views

Show that any open cover of a subset of the plane has a countable subcover.

Published on 13 Apr 2026 - 19:37

List Question

If $|z| = 1, z \in \mathbb{C}$, what can you say about the real and imaginary parts of $z^i$

Am I combining Cauchy and Taylor theorems to prove this Taylor representation correctly?

Unique Representation of Elements in the Complex Circle Group

Integrating $\int_{C(0,1)} \frac{1}{(z-a)(z-b)}dz$ for various cases of a and b being/not being in C

Montel's theorem to show normal family

Prove the radius of convergence of the complex power series $(z^2 - 1)/(z^3-1)$ about $z =2$ is sqrt(7)

Is the integral $\int_{-\infty}^{\infty}\frac{\sin(x)}{x^2}dx$ equal to zero?

Give the largest open set where the function $f(z)=\sum_{n=1}^{\infty} ne^{nz}$

A nonvanishing entire function of finite order is the logarithm of a polynomial

To Prove that $\ f(z)=cz^n$

Donald Sarason's problem X.20.3

Is it always true that $Log(z^{-1})=-Log(z)$

An expression for sin(40)

Show that a sequence having a finite limit point cannot approach \infty

Show that any open cover of a subset of the plane has a countable subcover.

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