Question

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

score 662 · Answer 1 · 2026-03-23 04:43:33

662

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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 23 Mar 2026 - 4:43

score 39 · Answer 2 · 2018-01-29 10:21:50

39

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

Published on 29 Jan 2018 - 10:21

score 2.2k · Answer 3 · 2018-01-29 11:31:18

2.2k

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

Published on 29 Jan 2018 - 11:31

score 203 · Answer 4 · 2026-03-17 05:15:51

203

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determination of a circle in the complex plane

Published on 17 Mar 2026 - 5:15

score 52 · Answer 5 · 2018-01-29 17:57:03

52

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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 Jan 2018 - 17:57

score 210 · Answer 6 · 2026-03-25 08:03:57

210

Views

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

Published on 25 Mar 2026 - 8:03

score 67 · Answer 7 · 2018-01-29 22:00:08

67

Views

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

Published on 29 Jan 2018 - 22:00

score 265 · Answer 8 · 2026-03-25 01:30:08

265

Views

Why are imaginary numbers defined the way they are?

Published on 25 Mar 2026 - 1:30

score 188 · Answer 9 · 2026-03-25 01:23:55

188

Views

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

Published on 25 Mar 2026 - 1:23

score 73 · Answer 10 · 2026-03-25 15:47:05

73

Views

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

Published on 25 Mar 2026 - 15:47

score 297 · Answer 11 · 2018-01-30 10:59:00

297

Views

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

Published on 30 Jan 2018 - 10:59

score 141 · Answer 12 · 2026-03-17 19:34:42

141

Views

Is there any intermediate fields between these two fields？

Published on 17 Mar 2026 - 19:34

score 69 · Answer 13 · 2018-01-30 14:36:37

69

Views

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

Published on 30 Jan 2018 - 14:36

score 334 · Answer 14 · 2026-03-25 01:17:35

334

Views

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

Published on 25 Mar 2026 - 1:17

score 4.9k · Answer 15 · 2018-01-30 22:22:46

4.9k

Views

Imaginary to the power of fractional number

Published on 30 Jan 2018 - 22:22

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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