Question

Prove that $|a + b| = |a| + |b| \iff a\overline{b} \ge 0$

score 104 · Answer 1 · 2026-04-15 20:18:34

104

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Prove that $|a + b| = |a| + |b| \iff a\overline{b} \ge 0$

Published on 15 Apr 2026 - 20:18

score 151 · Answer 2 · 2026-05-14 18:20:56

151

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Question about step in Ahlfors' proof of Cauchy's inequality in complex analysis.

Published on 14 May 2026 - 18:20

score 115 · Answer 3 · 2026-04-16 07:50:32

115

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Constraints on $x^2 + b x + c = 0$ such that at least one root has a positive real part

Published on 16 Apr 2026 - 7:50

score 876 · Answer 4 · 2026-05-10 16:32:54

876

Views

What properties a matrix need to satisfy to form a real vector space

Published on 10 May 2026 - 16:32

score 120 · Answer 5 · 2026-04-10 14:25:11

120

Views

Closed curve not passing origin and winding number (complex analysis)

Published on 10 Apr 2026 - 14:25

score 133 · Answer 6 · 2026-04-17 08:52:39

133

Views

Calculate residues at all isolated singularities of $f(z)=\frac{z^2+4}{(z+2)(z^2+1)^2}$.

Published on 17 Apr 2026 - 8:52

score 79 · Answer 7 · 2026-04-16 04:34:16

79

Views

If $|{z}|=\max\big\{|{z}+2|,|{z}-2|\big\}$, then which is true: $|z\pm \bar{z}|=2$ or $|z\pm \bar{z}|=1/2$?

Published on 16 Apr 2026 - 4:34

score 45 · Answer 8 · 2026-04-08 16:56:38

45

Views

How to solve equation ${z^3 = i}$ in the complex plane using polar form?

Published on 08 Apr 2026 - 16:56

score 47 · Answer 9 · 2026-04-16 21:02:20

47

Views

Show that the residue is $c_{-1}=-\frac{q''(z_0)}{(q'(z_0))^3}$.

Published on 16 Apr 2026 - 21:02

score 80 · Answer 10 · 2026-04-16 18:45:09

80

Views

Polar form of $\frac{2(1+i)(1-i\sqrt{3})}{(-\sqrt{3}+i)^{30}}$

Published on 16 Apr 2026 - 18:45

score 297 · Answer 11 · 2026-04-11 19:01:25

297

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What is the value of $1 -\omega^h + \omega^{2h} -...+(-1)^{n-1} \omega^{(n-1)h}$ when $\omega$ is a root of unity?

Published on 11 Apr 2026 - 19:01

score 228 · Answer 12 · 2026-04-10 16:35:59

Suppose $z$ and $\omega$ are two complex numbers such that $|z|≤1$ and $|\omega|≤1$ and $|z+i\omega|=|z-i\omega|=2$. Find $|z|$ and $|\omega|$.

score 377 · Answer 13 · 2026-04-14 19:30:47

377

Views

Solving the system $\cos x+\cos y+\cos z=\frac32\sqrt3$, $\sin x+\sin y+\sin z=\frac32$

Published on 14 Apr 2026 - 19:30

score 86 · Answer 14 · 2026-04-17 05:30:12

86

Views

existential theorem about Trigonometric Interpolation

Published on 17 Apr 2026 - 5:30

score 74 · Answer 15 · 2026-04-14 17:08:03

74

Views

If part of a polynomial has complex roots then is it necessary that this polynomial must have complex roots?

Published on 14 Apr 2026 - 17:08

List Question

Prove that $|a + b| = |a| + |b| \iff a\overline{b} \ge 0$

Question about step in Ahlfors' proof of Cauchy's inequality in complex analysis.

Constraints on $x^2 + b x + c = 0$ such that at least one root has a positive real part

What properties a matrix need to satisfy to form a real vector space

Closed curve not passing origin and winding number (complex analysis)

Calculate residues at all isolated singularities of $f(z)=\frac{z^2+4}{(z+2)(z^2+1)^2}$.

If $|{z}|=\max\big\{|{z}+2|,|{z}-2|\big\}$, then which is true: $|z\pm \bar{z}|=2$ or $|z\pm \bar{z}|=1/2$?

How to solve equation ${z^3 = i}$ in the complex plane using polar form?

Show that the residue is $c_{-1}=-\frac{q''(z_0)}{(q'(z_0))^3}$.

Polar form of $\frac{2(1+i)(1-i\sqrt{3})}{(-\sqrt{3}+i)^{30}}$

What is the value of $1 -\omega^h + \omega^{2h} -...+(-1)^{n-1} \omega^{(n-1)h}$ when $\omega$ is a root of unity?

Suppose $z$ and $\omega$ are two complex numbers such that $|z|≤1$ and $|\omega|≤1$ and $|z+i\omega|=|z-i\omega|=2$. Find $|z|$ and $|\omega|$.

Solving the system $\cos x+\cos y+\cos z=\frac32\sqrt3$, $\sin x+\sin y+\sin z=\frac32$

existential theorem about Trigonometric Interpolation

If part of a polynomial has complex roots then is it necessary that this polynomial must have complex roots?

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