Question

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

score 668 · Answer 1 · 2026-05-06 08:29:10

668

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Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

Published on 06 May 2026 - 8:29

score 41 · Answer 2 · 2026-04-15 00:35:27

41

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plot the set $M:= \{z \in \mathbb{C}; Im \left( \frac{z+i}{z-2} \right) = 0\}$

Published on 15 Apr 2026 - 0:35

score 2.2k · Answer 3 · 2026-04-14 04:01:39

2.2k

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Proving that a three complex numbers form an equilateral triangle with vertices on unit circle

Published on 14 Apr 2026 - 4:01

score 208 · Answer 4 · 2026-04-29 12:54:12

208

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determination of a circle in the complex plane

Published on 29 Apr 2026 - 12:54

score 56 · Answer 5 · 2026-04-29 12:52:47

56

Views

Prove/Disprove$ \langle f,f\rangle = 2\int_0^{0.5} \left | f(t) \right |^2 \, dt -\int_{0.5}^1 \left | f(t) \right |^2 \, dt = 0 \Rightarrow f = 0$

Published on 29 Apr 2026 - 12:52

score 215 · Answer 6 · 2026-05-10 20:04:14

215

Views

Complex numbers - $z^{2} = 4i$

Published on 10 May 2026 - 20:04

score 69 · Answer 7 · 2026-04-14 17:54:26

69

Views

Searchingthe polar form of $z = 2+i(1+\sqrt{3})$

Published on 14 Apr 2026 - 17:54

score 267 · Answer 8 · 2026-04-14 05:03:56

267

Views

Why are imaginary numbers defined the way they are?

Published on 14 Apr 2026 - 5:03

score 192 · Answer 9 · 2026-05-10 14:05:55

192

Views

Converting a taylor series with complex numbers to sigma notation: $x + (1+x^2)^(1/2)$

Published on 10 May 2026 - 14:05

score 75 · Answer 10 · 2026-04-15 12:23:47

75

Views

Finding minimum of $\max(\arg(a),\arg(b),\arg(c))$ in complex number

Published on 15 Apr 2026 - 12:23

score 300 · Answer 11 · 2026-04-13 23:22:42

300

Views

Finding all solutions of $x$ in $\sin(\pi x)+x=0$.

Published on 13 Apr 2026 - 23:22

score 149 · Answer 12 · 2026-04-29 12:49:12

149

Views

Is there any intermediate fields between these two fields？

Published on 29 Apr 2026 - 12:49

score 72 · Answer 13 · 2026-04-16 13:19:21

72

Views

Value of $f(-1)$ where $f(x) =x^{2/3}$.

Published on 16 Apr 2026 - 13:19

score 337 · Answer 14 · 2026-05-10 12:34:45

337

Views

Is it true that one can't raise both sides of an equation to a complex power?

Published on 10 May 2026 - 12:34

score 4.9k · Answer 15 · 2026-04-12 21:13:23

4.9k

Views

Imaginary to the power of fractional number

Published on 12 Apr 2026 - 21:13

List Question

Proving that $P:\mathbb{C}\rightarrow\mathbb{R}$, defined by $P(z)=Re(z)$ is open but is not closed.

plot the set $M:= \{z \in \mathbb{C}; Im \left( \frac{z+i}{z-2} \right) = 0\}$

Proving that a three complex numbers form an equilateral triangle with vertices on unit circle

determination of a circle in the complex plane

Prove/Disprove$ \langle f,f\rangle = 2\int_0^{0.5} \left | f(t) \right |^2 \, dt -\int_{0.5}^1 \left | f(t) \right |^2 \, dt = 0 \Rightarrow f = 0$

Complex numbers - $z^{2} = 4i$

Searchingthe polar form of $z = 2+i(1+\sqrt{3})$

Why are imaginary numbers defined the way they are?

Converting a taylor series with complex numbers to sigma notation: $x + (1+x^2)^(1/2)$

Finding minimum of $\max(\arg(a),\arg(b),\arg(c))$ in complex number

Finding all solutions of $x$ in $\sin(\pi x)+x=0$.

Is there any intermediate fields between these two fields？

Value of $f(-1)$ where $f(x) =x^{2/3}$.

Is it true that one can't raise both sides of an equation to a complex power?

Imaginary to the power of fractional number

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