Question

if $w$ is a complex number, how to show that $w^\left(1/2\right)$ has 2 roots? except the case for $w=0$

score 59 · Answer 1 · 2026-04-16 14:26:52

59

Views

if $w$ is a complex number, how to show that $w^\left(1/2\right)$ has 2 roots? except the case for $w=0$

Published on 16 Apr 2026 - 14:26

score 103 · Answer 2 · 2026-03-25 13:42:09

103

Views

Some identity related to Euler's identity

Published on 25 Mar 2026 - 13:42

score 79 · Answer 3 · 2026-04-10 07:39:20

79

Views

How to display $\sqrt{-i}$ (square root of a negative imaginary) in publication?

Published on 10 Apr 2026 - 7:39

score 60 · Answer 4 · 2026-04-17 05:26:37

60

Views

Prove that $|Re(z_{1})-Re(z_{2})|\leq |z_{1}-z_{2}|\leq |Re(z_{1})-Re(z_{2})|+|Im(z_{1})-Im(z_{2})|$.

Published on 17 Apr 2026 - 5:26

score 589 · Answer 5 · 2026-04-12 01:10:51

589

Views

limit of modulus of z over z approach infinity in complex plane

Published on 12 Apr 2026 - 1:10

score 67 · Answer 6 · 2026-04-10 16:06:50

67

Views

Why does Natural Log exhibits such behaviour with negative numbers?

Published on 10 Apr 2026 - 16:06

score 158 · Answer 7 · 2026-03-25 09:39:43

158

Views

Is there any integer solution for $\operatorname{Re}(a+bi)^n=\pm1$, where $n\geq 2$, except $(a,b)=(\pm1,0),(0,\pm1)$?

Published on 25 Mar 2026 - 9:39

score 65 · Answer 8 · 2026-04-14 16:29:09

65

Views

Given $ \mid x - y \mid = 1$ and equality predicates in $ \mathbb{C} $.How to get $ \mid x - y \mid = \frac{1}{2} $?

Published on 14 Apr 2026 - 16:29

score 231 · Answer 9 · 2026-04-25 12:22:45

231

Views

Conceptual question about complex roots of a polynomial

Published on 25 Apr 2026 - 12:22

score 93 · Answer 10 · 2026-04-13 20:17:30

93

Views

For $w\in\mathbb{C}$, prove that $w^3$ lies on the line passing through 1 and $w$ in the complex plane iff $\Re(w)=-\frac12$.

Published on 13 Apr 2026 - 20:17

score 80 · Answer 11 · 2026-04-09 20:43:05

80

Views

Why is $\frac{e^{i\pi n/50} + 1}{e^{i\pi n/50}-1} = \frac{e^{i\pi n/100} + e^{-i\pi n/100}}{e^{i\pi n/100} - e^{i\pi n/100}}$

Published on 09 Apr 2026 - 20:43

score 813 · Answer 12 · 2026-03-25 09:38:46

813

Views

Can $\operatorname{Re}(a+bi)^{n}$ be overlapped with $a,b\in\mathbb{Z}$ fixed?

Published on 25 Mar 2026 - 9:38

score 52 · Answer 13 · 2026-04-16 23:43:27

52

Views

Trying to prove that $\left|z-(z^2+1)^{\frac{1}{2}}\right| < 1$ for $Re(z)>0$.

Published on 16 Apr 2026 - 23:43

score 546 · Answer 14 · 2026-03-25 18:53:49

546

Views

Continuous transformation of upper half-plane to unit disk

Published on 25 Mar 2026 - 18:53

score 416 · Answer 15 · 2026-04-16 13:54:34

416

Views

Solve complex equation $4\cos(z)+5=0$

Published on 16 Apr 2026 - 13:54

List Question

if $w$ is a complex number, how to show that $w^\left(1/2\right)$ has 2 roots? except the case for $w=0$

Some identity related to Euler's identity

How to display $\sqrt{-i}$ (square root of a negative imaginary) in publication?

Prove that $|Re(z_{1})-Re(z_{2})|\leq |z_{1}-z_{2}|\leq |Re(z_{1})-Re(z_{2})|+|Im(z_{1})-Im(z_{2})|$.

limit of modulus of z over z approach infinity in complex plane

Why does Natural Log exhibits such behaviour with negative numbers?

Is there any integer solution for $\operatorname{Re}(a+bi)^n=\pm1$, where $n\geq 2$, except $(a,b)=(\pm1,0),(0,\pm1)$?

Given $ \mid x - y \mid = 1$ and equality predicates in $ \mathbb{C} $.How to get $ \mid x - y \mid = \frac{1}{2} $?

Conceptual question about complex roots of a polynomial

For $w\in\mathbb{C}$, prove that $w^3$ lies on the line passing through 1 and $w$ in the complex plane iff $\Re(w)=-\frac12$.

Why is $\frac{e^{i\pi n/50} + 1}{e^{i\pi n/50}-1} = \frac{e^{i\pi n/100} + e^{-i\pi n/100}}{e^{i\pi n/100} - e^{i\pi n/100}}$

Can $\operatorname{Re}(a+bi)^{n}$ be overlapped with $a,b\in\mathbb{Z}$ fixed?

Trying to prove that $\left|z-(z^2+1)^{\frac{1}{2}}\right| < 1$ for $Re(z)>0$.

Continuous transformation of upper half-plane to unit disk

Solve complex equation $4\cos(z)+5=0$

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