Question

$\frac{x^2}{a^2+ \lambda}+ \frac{y^2}{b^2+\lambda}=1$ family with $-a^2< \lambda < -b^2$ orthogonal to family with $\lambda > -b^2>-a^2$

score 134 · Answer 1 · 2026-04-14 22:54:09

$\frac{x^2}{a^2+ \lambda}+ \frac{y^2}{b^2+\lambda}=1$ family with $-a^2< \lambda < -b^2$ orthogonal to family with $\lambda > -b^2>-a^2$

score 116 · Answer 2 · 2026-03-25 14:26:56

116

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What do the Cauchy-Riemann equations tell us about being differentiable on a non-open subset?

Published on 25 Mar 2026 - 14:26

score 92 · Answer 3 · 2026-04-13 16:34:19

92

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Solve for all complex numbers z that satisfy the equation

Published on 13 Apr 2026 - 16:34

score 1.7k · Answer 4 · 2026-04-15 03:35:47

1.7k

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Let $z$ be a complex number of maximum amplitude satisfying $\vert z-3\vert=Re(z)$

Published on 15 Apr 2026 - 3:35

score 302 · Answer 5 · 2026-04-11 14:57:35

302

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Can a complex positive definite matrix be a unitary matrix?

Published on 11 Apr 2026 - 14:57

score 141 · Answer 6 · 2026-03-25 01:28:05

141

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Prove $[z^{1/2}]$ has no holomorphic branch on any open ball $B(0,R)$

Published on 25 Mar 2026 - 1:28

score 72 · Answer 7 · 2026-04-14 17:20:37

72

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Finding $\sum_{k=0}^{6}a_{3k} $ where $(x^2-x+1)^{10}=\sum_{k=0}^{20}a_k x^k$

Published on 14 Apr 2026 - 17:20

score 628 · Answer 8 · 2026-04-14 01:59:37

628

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How to determine the signature of a Hermitian form

Published on 14 Apr 2026 - 1:59

score 281 · Answer 9 · 2026-04-15 19:43:34

$f$ is an analytic function in $\mathbb C$. Prove or disprove that if $f(z)=f(3z)$ then $f(z)=C$, while $C$ is constant complex number.

score 414 · Answer 10 · 2026-04-11 09:53:20

414

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complex numbers (Z - i / Z+i )^5 = 1

Published on 11 Apr 2026 - 9:53

score 61 · Answer 11 · 2026-04-11 21:07:58

61

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How is this matrix being transformed?

Published on 11 Apr 2026 - 21:07

score 143 · Answer 12 · 2026-04-09 11:07:00

143

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Complex Solution to Integral of sec(x)

Published on 09 Apr 2026 - 11:07

score 77 · Answer 13 · 2026-04-16 20:34:04

$A=\bigl\{z:\arg\left(\frac{z-1}{z}\right)=\frac{π}{2}\bigr\}$ and $B=\{z:\arg\left(z-1\right)=π\}$. Find $(A\;\cap\;B)$.

score 157 · Answer 14 · 2026-03-27 13:03:22

157

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Find all $p\in \mathbb{C}[x]$ with $p(0)=1$ such that $p(z)\leq 1 \forall z$ with $|z|=1$.

Published on 27 Mar 2026 - 13:03

score 342 · Answer 15 · 2026-04-11 09:21:34

342

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Question involving de Moivre identity and writing $\cos4\theta$ in terms of complex numbers

Published on 11 Apr 2026 - 9:21

List Question

$\frac{x^2}{a^2+ \lambda}+ \frac{y^2}{b^2+\lambda}=1$ family with $-a^2< \lambda < -b^2$ orthogonal to family with $\lambda > -b^2>-a^2$

What do the Cauchy-Riemann equations tell us about being differentiable on a non-open subset?

Solve for all complex numbers z that satisfy the equation

Let $z$ be a complex number of maximum amplitude satisfying $\vert z-3\vert=Re(z)$

Can a complex positive definite matrix be a unitary matrix?

Prove $[z^{1/2}]$ has no holomorphic branch on any open ball $B(0,R)$

Finding $\sum_{k=0}^{6}a_{3k} $ where $(x^2-x+1)^{10}=\sum_{k=0}^{20}a_k x^k$

How to determine the signature of a Hermitian form

$f$ is an analytic function in $\mathbb C$. Prove or disprove that if $f(z)=f(3z)$ then $f(z)=C$, while $C$ is constant complex number.

complex numbers (Z - i / Z+i )^5 = 1

How is this matrix being transformed?

Complex Solution to Integral of sec(x)

$A=\bigl\{z:\arg\left(\frac{z-1}{z}\right)=\frac{π}{2}\bigr\}$ and $B=\{z:\arg\left(z-1\right)=π\}$. Find $(A\;\cap\;B)$.

Find all $p\in \mathbb{C}[x]$ with $p(0)=1$ such that $p(z)\leq 1 \forall z$ with $|z|=1$.

Question involving de Moivre identity and writing $\cos4\theta$ in terms of complex numbers

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