List questions from complex-numbers

51

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If $f(0) = \pi i$ and $e^{Re f(z)} \leq 1$ for all $|z| < 1,$ then $f(z) = \pi i$ for all $z \in D.$

Published on 15 Apr 2026 - 17:56

488

Views

Average squared absolute value of inner product between some unit vectors in a Hilbert space

Published on 13 Apr 2026 - 16:53

243

Views

Find all values in polar form.

Published on 15 Apr 2026 - 11:17

297

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Find $e^{(\pi/2) e^{(\pi/2) e^{\cdots}}}$

Published on 14 Apr 2026 - 0:26

412

Views

Finding complex Fourier series of $f(x) = x$

Published on 11 Apr 2026 - 17:49

33

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Find all the real subspaces $W$ of $V$ satisfying the properties.

Published on 13 Apr 2026 - 4:10

44

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Find the relationship between and (complex numbers)

Published on 08 Apr 2026 - 19:33

126

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Exclusion of certain points of a complex locus

Published on 26 Mar 2026 - 3:11

979

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Are there more rectangles than squares?

Published on 09 Apr 2026 - 7:36

227

Views

Finding the range of $\arg(1-z)$ when $|z|<1$.

Published on 14 Apr 2026 - 11:01

73

Views

Complex number problem using binomial Series

Published on 10 Apr 2026 - 10:18

84

Views

Finding a quadratic equation with roots $x=α^2$ and $x=β^2$

Published on 11 Apr 2026 - 11:06

70

Views

Is ${(-1)}^{\frac{1}{6}}=i$?

Published on 14 Apr 2026 - 23:24

72

Views

Why does this pattern occur on this plot?

Published on 14 Apr 2026 - 2:52

140

Views

Conditions for $z \in \mathbb{C} \backslash \{ 0 \}$ and $\alpha \in \mathbb{C}$ such that $z^\alpha = \exp(\alpha \log z)$

Published on 14 Apr 2026 - 12:28

List Question

If $f(0) = \pi i$ and $e^{Re f(z)} \leq 1$ for all $|z| < 1,$ then $f(z) = \pi i$ for all $z \in D.$

Average squared absolute value of inner product between some unit vectors in a Hilbert space

Find all values in polar form.

Find $e^{(\pi/2) e^{(\pi/2) e^{\cdots}}}$

Finding complex Fourier series of $f(x) = x$

Find all the real subspaces $W$ of $V$ satisfying the properties.

Find the relationship between and (complex numbers)

Exclusion of certain points of a complex locus

Are there more rectangles than squares?

Finding the range of $\arg(1-z)$ when $|z|<1$.

Complex number problem using binomial Series

Finding a quadratic equation with roots $x=α^2$ and $x=β^2$

Is ${(-1)}^{\frac{1}{6}}=i$?

Why does this pattern occur on this plot?

Conditions for $z \in \mathbb{C} \backslash \{ 0 \}$ and $\alpha \in \mathbb{C}$ such that $z^\alpha = \exp(\alpha \log z)$

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