Question

$\Im\left ((a+bi)^n\right )=0, a,b \in \mathbb{R}, n \in \mathbb{N^*}$

score 46 · Answer 1 · 2026-04-16 07:33:33

46

Views

$\Im\left ((a+bi)^n\right )=0, a,b \in \mathbb{R}, n \in \mathbb{N^*}$

Published on 16 Apr 2026 - 7:33

score 107 · Answer 2 · 2026-04-09 18:33:24

107

Views

What is the generalized definition of '<' and '>' for complex numbers?

Published on 09 Apr 2026 - 18:33

score 25 · Answer 3 · 2026-04-16 07:02:12

25

Views

If $\lim_{n \to ∞} z_n=L_1$ then $\lim_{n \to ∞} \overline{z_n}=\overline{L_1}$ for $z_n \in \mathbb{C}$

Published on 16 Apr 2026 - 7:02

score 213 · Answer 4 · 2026-04-10 13:47:44

213

Views

Imaginary Numbers

Published on 10 Apr 2026 - 13:47

score 74 · Answer 5 · 2026-04-17 15:29:37

74

Views

Why does $2x_1x_2y_1y_2 \leq x_1^2y_2^2+x_2^2y_1^2$?

Published on 17 Apr 2026 - 15:29

score 9.3k · Answer 6 · 2026-04-16 21:10:06

9.3k

Views

Find all complex and real roots of higher degree polynomials, given one root

Published on 16 Apr 2026 - 21:10

score 67 · Answer 7 · 2026-04-15 03:52:23

67

Views

All Values of a Complex expression

Published on 15 Apr 2026 - 3:52

score 1.8k · Answer 8 · 2026-04-17 15:05:21

Proving $\left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin n\left(\frac{\pi }{2-x}\right)$

score 916 · Answer 9 · 2026-04-13 22:32:42

916

Views

Is $\{z\in\mathbb C\mid|\text{Re }z|+|\text{Im }z|\le1\}$ open or closed?

Published on 13 Apr 2026 - 22:32

score 212 · Answer 10 · 2026-04-13 11:50:55

212

Views

Can anyone tell me how $\frac{\pi}{\sqrt 2} = \frac{\pi + i\pi}{2\sqrt i}$

Published on 13 Apr 2026 - 11:50

score 359 · Answer 11 · 2026-04-10 19:44:34

359

Views

Principal branch of the complex logarithm does not always satisfy the product formula

Published on 10 Apr 2026 - 19:44

score 34 · Answer 12 · 2026-04-13 20:17:27

34

Views

Is this log identity true?

Published on 13 Apr 2026 - 20:17

score 45 · Answer 13 · 2026-04-10 08:35:38

45

Views

Function with exponent imaginary power

Published on 10 Apr 2026 - 8:35

score 299 · Answer 14 · 2026-04-09 13:58:24

299

Views

When equality holds in an inequality

Published on 09 Apr 2026 - 13:58

score 120 · Answer 15 · 2026-04-14 13:35:54

120

Views

$f:U \rightarrow \mathbb{C} $ is continuous on $U$ if and only if {$z \in U| f(z)\in V$} is open for every open set V in $\mathbb{C}$

Published on 14 Apr 2026 - 13:35

List Question

$\Im\left ((a+bi)^n\right )=0, a,b \in \mathbb{R}, n \in \mathbb{N^*}$

What is the generalized definition of '<' and '>' for complex numbers?

If $\lim_{n \to ∞} z_n=L_1$ then $\lim_{n \to ∞} \overline{z_n}=\overline{L_1}$ for $z_n \in \mathbb{C}$

Imaginary Numbers

Why does $2x_1x_2y_1y_2 \leq x_1^2y_2^2+x_2^2y_1^2$?

Find all complex and real roots of higher degree polynomials, given one root

All Values of a Complex expression

Proving $\left(\frac{1+\sin x+i\cos x}{1+\sin x-i\cos x}\right)^n=\cos n\left(\frac{\pi }{2}-x\right)+i\sin n\left(\frac{\pi }{2-x}\right)$

Is $\{z\in\mathbb C\mid|\text{Re }z|+|\text{Im }z|\le1\}$ open or closed?

Can anyone tell me how $\frac{\pi}{\sqrt 2} = \frac{\pi + i\pi}{2\sqrt i}$

Principal branch of the complex logarithm does not always satisfy the product formula

Is this log identity true?

Function with exponent imaginary power

When equality holds in an inequality

$f:U \rightarrow \mathbb{C} $ is continuous on $U$ if and only if {$z \in U| f(z)\in V$} is open for every open set V in $\mathbb{C}$

Trending Questions

Popular # Hahtags

Popular Questions