Question

Proof Strategy: For all nonzero complex numbers $z$ and all nonzero rational numbers $a$ and $b, \mathbb Q (az+b)=\mathbb Q(z)$

score 72 · Answer 1 · 2026-04-15 06:24:25

72

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Proof Strategy: For all nonzero complex numbers $z$ and all nonzero rational numbers $a$ and $b, \mathbb Q (az+b)=\mathbb Q(z)$

Published on 15 Apr 2026 - 6:24

score 322 · Answer 2 · 2026-04-17 04:51:00

322

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$\text{If } |z_1| = |z_2|, \text{ show that } \frac{z_1 + z_2}{z_1-z_2} \text{is imaginary.} $

Published on 17 Apr 2026 - 4:51

score 115 · Answer 3 · 2026-04-16 19:27:44

115

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How $\sqrt{\cos (106.3) + i \sin (106.3)} = \cos 53.15 + i \sin 53.15$

Published on 16 Apr 2026 - 19:27

score 17.7k · Answer 4 · 2026-04-17 09:35:37

17.7k

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By using De Moivre's Theorem, show that $\cos5\theta = 16\cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta$

Published on 17 Apr 2026 - 9:35

score 131 · Answer 5 · 2026-04-14 06:44:07

131

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Proving that an analytic function that maps on to {$z\in \mathbb{C}| |z-2|=1$} from some connected open set is constant

Published on 14 Apr 2026 - 6:44

score 118 · Answer 6 · 2026-04-12 14:39:26

118

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Linear Algebra - args complex number question

Published on 12 Apr 2026 - 14:39

score 2k · Answer 7 · 2026-04-10 16:46:32

2k

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Condition for 3 complex numbers to represent an equilateral triangle

Published on 10 Apr 2026 - 16:46

score 109 · Answer 8 · 2026-04-09 23:32:27

109

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How can I simplify the polynomial $x^4+1$ into quadratic factors?

Published on 09 Apr 2026 - 23:32

score 3k · Answer 9 · 2026-04-14 01:39:58

3k

Views

Complex conjugate to the power proof

Published on 14 Apr 2026 - 1:39

score 1.5k · Answer 10 · 2026-04-11 06:14:20

1.5k

Views

Does $2^i$ exist, if so how do I calculate its value?

Published on 11 Apr 2026 - 6:14

score 100 · Answer 11 · 2026-04-09 06:34:53

100

Views

Complex numbers proof problem

Published on 09 Apr 2026 - 6:34

score 205 · Answer 12 · 2026-04-13 11:46:43

205

Views

Branches of complex logarithmic function

Published on 13 Apr 2026 - 11:46

score 98 · Answer 13 · 2026-04-08 10:55:27

98

Views

Complex exponent problem

Published on 08 Apr 2026 - 10:55

score 183 · Answer 14 · 2026-04-09 12:20:51

183

Views

Prove that the following function tends to infinity as z approaches i (complex analysis)?

Published on 09 Apr 2026 - 12:20

score 565 · Answer 15 · 2026-04-15 18:11:13

565

Views

for $z,w\in\mathbb{C}$, $\sqrt{zw} = \sqrt{z}\sqrt{w}$?

Published on 15 Apr 2026 - 18:11

List Question

Proof Strategy: For all nonzero complex numbers $z$ and all nonzero rational numbers $a$ and $b, \mathbb Q (az+b)=\mathbb Q(z)$

$\text{If } |z_1| = |z_2|, \text{ show that } \frac{z_1 + z_2}{z_1-z_2} \text{is imaginary.} $

How $\sqrt{\cos (106.3) + i \sin (106.3)} = \cos 53.15 + i \sin 53.15$

By using De Moivre's Theorem, show that $\cos5\theta = 16\cos^5 \theta - 20 \cos^3 \theta + 5 \cos \theta$

Proving that an analytic function that maps on to {$z\in \mathbb{C}| |z-2|=1$} from some connected open set is constant

Linear Algebra - args complex number question

Condition for 3 complex numbers to represent an equilateral triangle

How can I simplify the polynomial $x^4+1$ into quadratic factors?

Complex conjugate to the power proof

Does $2^i$ exist, if so how do I calculate its value?

Complex numbers proof problem

Branches of complex logarithmic function

Complex exponent problem

Prove that the following function tends to infinity as z approaches i (complex analysis)?

for $z,w\in\mathbb{C}$, $\sqrt{zw} = \sqrt{z}\sqrt{w}$?

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