Question

Proof that $\frac{e^{\frac{\pi i}{4}}}{\sqrt{2}}\left(1+e^{-(2n+1)\frac{\pi i}{2}}\right)-e^{\frac{n^2\pi i}{2}}=0$

score 123 · Answer 1 · 2026-04-18 12:58:46

123

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Proof that $\frac{e^{\frac{\pi i}{4}}}{\sqrt{2}}\left(1+e^{-(2n+1)\frac{\pi i}{2}}\right)-e^{\frac{n^2\pi i}{2}}=0$

Published on 18 Apr 2026 - 12:58

score 280 · Answer 2 · 2026-04-13 13:01:48

280

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Attempting to plot the period-3 boundary of the Mandelbrot Set in Desmos

Published on 13 Apr 2026 - 13:01

score 115 · Answer 3 · 2026-04-14 03:06:02

115

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What is $\lim_{z \to \infty} \frac{z^{2}-(2+3i)z+1}{iz-3}$?

Published on 14 Apr 2026 - 3:06

score 1.7k · Answer 4 · 2026-04-11 03:03:03

1.7k

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Sum of complex numbers in exponential form formula inconsistency

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score 521 · Answer 5 · 2026-05-16 08:18:43

521

Views

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score 200 · Answer 6 · 2026-04-10 08:55:55

200

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Published on 10 Apr 2026 - 8:55

score 80 · Answer 7 · 2026-04-16 03:41:02

80

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Published on 16 Apr 2026 - 3:41

score 61 · Answer 8 · 2026-04-12 14:41:32

61

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score 202 · Answer 9 · 2026-04-12 22:56:35

202

Views

How does one show that the residue of the first derivative of a holomorphic function is zero in its singularity?

Published on 12 Apr 2026 - 22:56

score 45 · Answer 10 · 2026-04-15 01:19:03

45

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If $\mathbf{v}\in\mathbb{C}^n$, does $\sum_{k=1}^{n}v_k^2$ has any specific name?

Published on 15 Apr 2026 - 1:19

score 356 · Answer 11 · 2026-04-10 12:06:17

356

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How to prove that $-|z| \le \Re (z) \le |z|$ and $-|z| \le \Im (z) \le |z|$?

Published on 10 Apr 2026 - 12:06

score 453 · Answer 12 · 2026-05-14 16:57:49

453

Views

Complex Number Proof Questions

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score 422 · Answer 13 · 2026-04-17 10:44:42

422

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Which integer combinations of $n$-th roots of unity are zero?

Published on 17 Apr 2026 - 10:44

score 119 · Answer 14 · 2026-04-11 11:03:26

119

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Published on 11 Apr 2026 - 11:03

score 157 · Answer 15 · 2026-04-17 10:37:11

157

Views

Given $\frac{z_1}{2z_2}+\frac{2z_2}{z_1} = i$ and $0, z_1, z_2$ form two triangles with $A, B$ the least angles of each. Find $\cot A +\cot B$

Published on 17 Apr 2026 - 10:37

List Question

Proof that $\frac{e^{\frac{\pi i}{4}}}{\sqrt{2}}\left(1+e^{-(2n+1)\frac{\pi i}{2}}\right)-e^{\frac{n^2\pi i}{2}}=0$

Attempting to plot the period-3 boundary of the Mandelbrot Set in Desmos

What is $\lim_{z \to \infty} \frac{z^{2}-(2+3i)z+1}{iz-3}$?

Sum of complex numbers in exponential form formula inconsistency

Finding Periodic/Fixed Points in the Julia Sets close to the Period-3 Cardioid

Characteristic function of real part of complex random variable

Find the range of $|3-i(z-1)|$

Complex number doubt

How does one show that the residue of the first derivative of a holomorphic function is zero in its singularity?

If $\mathbf{v}\in\mathbb{C}^n$, does $\sum_{k=1}^{n}v_k^2$ has any specific name?

How to prove that $-|z| \le \Re (z) \le |z|$ and $-|z| \le \Im (z) \le |z|$?

Complex Number Proof Questions

Which integer combinations of $n$-th roots of unity are zero?

Geometric intuition of perpendicular complex vectors

Given $\frac{z_1}{2z_2}+\frac{2z_2}{z_1} = i$ and $0, z_1, z_2$ form two triangles with $A, B$ the least angles of each. Find $\cot A +\cot B$

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