Question

How $|\phi| < 1$ and $|z| \leq 1$ is important to prove the convergence of the following power series

score 54 · Answer 1 · 2019-08-05 06:24:14

54

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How $|\phi| < 1$ and $|z| \leq 1$ is important to prove the convergence of the following power series

Published on 05 Aug 2019 - 6:24

score 153 · Answer 2 · 2026-03-25 20:36:41

153

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Find all integer $n$ such that there are complex $a$, $b$, $c$, $d$ satisfying $a^n=b^n=c^n=d^n=1$ and $a+b+c+d=1$.

Published on 25 Mar 2026 - 20:36

score 180 · Answer 3 · 2026-03-25 09:25:16

180

Views

why $x^{4} = 1 : x \in \mathbb{C}$ doesn't have infinite solutions?

Published on 25 Mar 2026 - 9:25

score 225 · Answer 4 · 2026-04-10 10:46:23

225

Views

Multiplicative norm on $\mathbb{C}$ inducing euclidean norm on $\mathbb{R}$

Published on 10 Apr 2026 - 10:46

score 55 · Answer 5 · 2019-08-06 04:39:59

55

Views

$2^{n-1} \prod^{n-1}_{k=1} (\cos \theta-\cos \frac{kπ}{n})= ??$

Published on 06 Aug 2019 - 4:39

score 38 · Answer 6 · 2026-04-11 01:50:52

38

Views

One complex function is giving two contradictory answers.

Published on 11 Apr 2026 - 1:50

score 121 · Answer 7 · 2026-03-30 03:23:34

121

Views

Domain of $7^{\log_7(x^2-4x+5)}$

Published on 30 Mar 2026 - 3:23

score 222 · Answer 8 · 2026-03-27 00:04:42

222

Views

all hyperbolic cyclic subgroup of P$SL(2, \mathbb{R})$ are Fuchsian.

Published on 27 Mar 2026 - 0:04

score 131 · Answer 9 · 2026-04-10 01:11:32

131

Views

Smooth maps from given manifold into the complex plane: is there a "product rule"?

Published on 10 Apr 2026 - 1:11

score 87 · Answer 10 · 2019-08-07 15:22:19

87

Views

Proof that $\arctan z+\arctan \frac{1}{z}$ does not depend on $\operatorname{Im}z$ when $\operatorname{Re}z\ne 0$ and $\operatorname{Im}z\ne 0$

Published on 07 Aug 2019 - 15:22

score 74 · Answer 11 · 2019-08-07 16:13:22

If $\arg\frac{z_1-z}{z-z_2}=\frac{\pi}{2}$, where $z_1=6+i$ and $z_2=4-3i$, then $\lvert z -(5-i)\rvert = \sqrt{5}$

score 264 · Answer 12 · 2026-03-27 23:32:04

264

Views

Proving $z^{2}+2z-1$ on the unit circle is a Cardioid.

Published on 27 Mar 2026 - 23:32

score 109 · Answer 13 · 2026-04-10 17:15:49

109

Views

How can I solve this Entrance Exam problem?

Published on 10 Apr 2026 - 17:15

score 670 · Answer 14 · 2026-04-03 12:38:12

670

Views

Polynomials, what are the values of "m" and "n"?

Published on 03 Apr 2026 - 12:38

score 109 · Answer 15 · 2026-03-28 11:34:17

109

Views

Why is $1=\sqrt{(-1)(-1)}=\sqrt{i^2\cdot i^2}=\sqrt{i^4}=\sqrt{\left(e^{i\frac{\pi}{2}}\right)^4}=\sqrt{e^{i2\pi}}=e^{i\pi}=-1$ wrong?

Published on 28 Mar 2026 - 11:34

List Question

How $|\phi| < 1$ and $|z| \leq 1$ is important to prove the convergence of the following power series

Find all integer $n$ such that there are complex $a$, $b$, $c$, $d$ satisfying $a^n=b^n=c^n=d^n=1$ and $a+b+c+d=1$.

why $x^{4} = 1 : x \in \mathbb{C}$ doesn't have infinite solutions?

Multiplicative norm on $\mathbb{C}$ inducing euclidean norm on $\mathbb{R}$

$2^{n-1} \prod^{n-1}_{k=1} (\cos \theta-\cos \frac{kπ}{n})= ??$

One complex function is giving two contradictory answers.

Domain of $7^{\log_7(x^2-4x+5)}$

all hyperbolic cyclic subgroup of P$SL(2, \mathbb{R})$ are Fuchsian.

Smooth maps from given manifold into the complex plane: is there a "product rule"?

Proof that $\arctan z+\arctan \frac{1}{z}$ does not depend on $\operatorname{Im}z$ when $\operatorname{Re}z\ne 0$ and $\operatorname{Im}z\ne 0$

If $\arg\frac{z_1-z}{z-z_2}=\frac{\pi}{2}$, where $z_1=6+i$ and $z_2=4-3i$, then $\lvert z -(5-i)\rvert = \sqrt{5}$

Proving $z^{2}+2z-1$ on the unit circle is a Cardioid.

How can I solve this Entrance Exam problem?

Polynomials, what are the values of "m" and "n"?

Why is $1=\sqrt{(-1)(-1)}=\sqrt{i^2\cdot i^2}=\sqrt{i^4}=\sqrt{\left(e^{i\frac{\pi}{2}}\right)^4}=\sqrt{e^{i2\pi}}=e^{i\pi}=-1$ wrong?

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