Question

Show that if $|z| = 3$ then $8 ≤ |3z^2 − 5z + 4i| ≤ 46$

score 889 · Answer 1 · 2018-08-23 02:55:31

889

Views

Show that if $|z| = 3$ then $8 ≤ |3z^2 − 5z + 4i| ≤ 46$

Published on 23 Aug 2018 - 2:55

score 37 · Answer 2 · 2018-08-23 04:39:07

$f(z) = 2z + 3\overline z$, show using the limit definition that $f$ is continuous at every point $a\in\mathbb C$.

score 95 · Answer 3 · 2026-03-27 00:05:13

95

Views

What is the name of the following theorem?

Published on 27 Mar 2026 - 0:05

score 116 · Answer 4 · 2026-03-25 01:31:11

116

Views

Visualizing and understanding the roots of $f(z) = z^2 - e^{i\varphi}$

Published on 25 Mar 2026 - 1:31

score 43 · Answer 5 · 2018-08-23 13:18:40

43

Views

Nature of equation of line $sz+t\bar z+r=0$, s,t and r are complex numbers

Published on 23 Aug 2018 - 13:18

score 2.2k · Answer 6 · 2026-03-26 17:25:46

2.2k

Views

Factoring $x^n + 1$.

Published on 26 Mar 2026 - 17:25

score 93 · Answer 7 · 2026-03-25 17:37:03

93

Views

How can i put a log inside an infinite sum?

Published on 25 Mar 2026 - 17:37

score 72 · Answer 8 · 2018-08-24 08:20:14

72

Views

Good treatment of Euler’s formula

Published on 24 Aug 2018 - 8:20

score 142 · Answer 9 · 2018-08-25 08:12:11

142

Views

Complex Number equation: $z+2\bar{z}= |\bar{z}+3|$

Published on 25 Aug 2018 - 8:12

score 1k · Answer 10 · 2026-03-25 04:41:09

1k

Views

What is the motivation for the development of dual numbers?

Published on 25 Mar 2026 - 4:41

score 69 · Answer 11 · 2026-03-26 07:56:47

69

Views

Determine what $\dim(X)$ is.

Published on 26 Mar 2026 - 7:56

score 355 · Answer 12 · 2018-08-25 21:22:54

355

Views

Showing that $G/G_m$ and $G/G_n$ are isomorphic groups.

Published on 25 Aug 2018 - 21:22

score 134 · Answer 13 · 2026-03-25 04:43:44

134

Views

Map from the upper half plane to a circle $\vert w-w_0\vert<R$ such that $T'(u_0+v_0i)>0$ and $T(i)=u_0+iv_0$

Published on 25 Mar 2026 - 4:43

score 185 · Answer 14 · 2026-03-26 17:33:31

185

Views

Replacing $b$ with $bi$ in $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ turns the ellipse equation into a hyperbola equation; is there a deep meaning to this?

Published on 26 Mar 2026 - 17:33

score 90 · Answer 15 · 2018-08-26 03:16:37

90

Views

If $f \colon X \to \mathbb{C}$ is continuous and $X \subset \mathbb{C}$ is closed and bounded then $f(X)$ is closed and bounded.

Published on 26 Aug 2018 - 3:16

List Question

Show that if $|z| = 3$ then $8 ≤ |3z^2 − 5z + 4i| ≤ 46$

$f(z) = 2z + 3\overline z$, show using the limit definition that $f$ is continuous at every point $a\in\mathbb C$.

What is the name of the following theorem?

Visualizing and understanding the roots of $f(z) = z^2 - e^{i\varphi}$

Nature of equation of line $sz+t\bar z+r=0$, s,t and r are complex numbers

Factoring $x^n + 1$.

How can i put a log inside an infinite sum?

Good treatment of Euler’s formula

Complex Number equation: $z+2\bar{z}= |\bar{z}+3|$

What is the motivation for the development of dual numbers?

Determine what $\dim(X)$ is.

Showing that $G/G_m$ and $G/G_n$ are isomorphic groups.

Map from the upper half plane to a circle $\vert w-w_0\vert<R$ such that $T'(u_0+v_0i)>0$ and $T(i)=u_0+iv_0$

Replacing $b$ with $bi$ in $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ turns the ellipse equation into a hyperbola equation; is there a deep meaning to this?

If $f \colon X \to \mathbb{C}$ is continuous and $X \subset \mathbb{C}$ is closed and bounded then $f(X)$ is closed and bounded.

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