Question

Show that $\frac 1z$ maps circle $|z-1|=1$ onto vertical line $x=\frac 12$

score 812 · Answer 1 · 2026-04-17 13:55:00

812

Views

Show that $\frac 1z$ maps circle $|z-1|=1$ onto vertical line $x=\frac 12$

Published on 17 Apr 2026 - 13:55

score 86 · Answer 2 · 2026-04-15 11:36:33

86

Views

Surjectivity and little Picard's theorem

Published on 15 Apr 2026 - 11:36

score 157 · Answer 3 · 2026-03-26 11:01:39

157

Views

Complex Numbers: How to find the number of solutions of $z^3 + \overline{z} = 0$

Published on 26 Mar 2026 - 11:01

score 29 · Answer 4 · 2026-04-12 15:26:18

29

Views

Complex numbers ,how to find argument

Published on 12 Apr 2026 - 15:26

score 51 · Answer 5 · 2026-04-09 09:10:21

51

Views

Convert complex to polar cord

Published on 09 Apr 2026 - 9:10

score 104 · Answer 6 · 2026-04-16 17:24:22

Show that complex numbers satisfying $z_1 + z_2 + z_3 = z_1^2 + z_2^2 + z_3^2 = 0$ have equal module $|z_1|=|z_2|=|z_3|$

score 117 · Answer 7 · 2026-04-11 22:49:29

117

Views

Sketching sets of complex numbers, e.g. $z=i$

Published on 11 Apr 2026 - 22:49

score 104 · Answer 8 · 2026-04-13 00:36:34

104

Views

Checking for convergence of $\sum_{n=1}^\infty \frac{(-i)^n}{n}$

Published on 13 Apr 2026 - 0:36

score 299 · Answer 9 · 2026-04-09 07:53:01

299

Views

Difficult exam question - finding complex numbers from a quadratic.

Published on 09 Apr 2026 - 7:53

score 165 · Answer 10 · 2026-04-15 20:15:23

Prove if $w=\cos{\frac{2\pi}{n}}+i\sin{\frac{2\pi}{n}}$ then the $n$ roots can be written as $1,w,w^2,...,w^{n-1}$

score 330 · Answer 11 · 2026-04-09 02:32:27

330

Views

How the does complex part cancel out in complex roots with Euler's formula?

Published on 09 Apr 2026 - 2:32

score 175 · Answer 12 · 2026-04-12 04:53:10

175

Views

Why is the derivative of the complex definition of sin(x) equal to icos(x)?

Published on 12 Apr 2026 - 4:53

score 59 · Answer 13 · 2026-04-09 08:16:21

59

Views

How do I solve this complex polynomial?

Published on 09 Apr 2026 - 8:16

score 100 · Answer 14 · 2026-04-11 07:55:59

100

Views

Paradox observed while studying Euler's formula

Published on 11 Apr 2026 - 7:55

score 395 · Answer 15 · 2026-03-25 23:37:43

395

Views

Real and positive sum of complex number in the unit circle

Published on 25 Mar 2026 - 23:37

List Question

Show that $\frac 1z$ maps circle $|z-1|=1$ onto vertical line $x=\frac 12$

Surjectivity and little Picard's theorem

Complex Numbers: How to find the number of solutions of $z^3 + \overline{z} = 0$

Complex numbers ,how to find argument

Convert complex to polar cord

Show that complex numbers satisfying $z_1 + z_2 + z_3 = z_1^2 + z_2^2 + z_3^2 = 0$ have equal module $|z_1|=|z_2|=|z_3|$

Sketching sets of complex numbers, e.g. $z=i$

Checking for convergence of $\sum_{n=1}^\infty \frac{(-i)^n}{n}$

Difficult exam question - finding complex numbers from a quadratic.

Prove if $w=\cos{\frac{2\pi}{n}}+i\sin{\frac{2\pi}{n}}$ then the $n$ roots can be written as $1,w,w^2,...,w^{n-1}$

How the does complex part cancel out in complex roots with Euler's formula?

Why is the derivative of the complex definition of sin(x) equal to icos(x)?

How do I solve this complex polynomial?

Paradox observed while studying Euler's formula

Real and positive sum of complex number in the unit circle

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