Question

Show that $\left| z + \sqrt{z^2 + c^2} \right| > c$ for $\operatorname{Re}(z) > 0$

score 65 · Answer 1 · 2019-06-19 19:17:59

65

Views

Show that $\left| z + \sqrt{z^2 + c^2} \right| > c$ for $\operatorname{Re}(z) > 0$

Published on 19 Jun 2019 - 19:17

score 45 · Answer 2 · 2026-03-26 21:25:53

45

Views

Find every $a \in \mathbb{R}$ such that $f = X^{2n+1} - (2n+1)X + a$ has a repeated root

Published on 26 Mar 2026 - 21:25

score 547 · Answer 3 · 2026-03-26 16:26:38

547

Views

Using roots of unity to find exact trig values

Published on 26 Mar 2026 - 16:26

score 189 · Answer 4 · 2026-03-28 00:36:46

189

Views

Ordering Complex Numbers

Published on 28 Mar 2026 - 0:36

score 185 · Answer 5 · 2019-06-21 08:48:21

185

Views

Find the complex square root of $7+6\sqrt2i$

Published on 21 Jun 2019 - 8:48

score 38 · Answer 6 · 2026-03-26 17:53:29

38

Views

Let $w \in G_{24}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $w^{15n} + \sum^{11}_{i=1} \overline{w}^{2i+6}$ is purely imaginary.

Published on 26 Mar 2026 - 17:53

score 156 · Answer 7 · 2026-03-28 09:30:42

156

Views

How to solve for imaginary roots of a quartic that cannot be factored and has no real roots?

Published on 28 Mar 2026 - 9:30

score 183 · Answer 8 · 2019-06-23 15:24:22

183

Views

Complex number confussion

Published on 23 Jun 2019 - 15:24

score 100 · Answer 9 · 2026-04-03 04:51:23

100

Views

What is $\sqrt [3]{-1}$ and how does one obtain its value?

Published on 03 Apr 2026 - 4:51

score 41 · Answer 10 · 2026-03-25 15:22:28

41

Views

Let $w\in G_{18}$ be a primitive root of unity. Prove that $w^{16} \sum_{j=1}^{17}(w^3 \overline{w})^{3j+1}$ is imaginary pure.

Published on 25 Mar 2026 - 15:22

score 103 · Answer 11 · 2026-04-08 18:29:38

103

Views

How to find this complex logarithm value without using a calculator?

Published on 08 Apr 2026 - 18:29

score 93 · Answer 12 · 2026-04-08 20:43:34

93

Views

Can constants be complex for integral table?

Published on 08 Apr 2026 - 20:43

score 175 · Answer 13 · 2026-03-29 14:59:12

175

Views

Find the polar representation of $z = \sin\theta+i(1+\cos\theta)$

Published on 29 Mar 2026 - 14:59

score 53 · Answer 14 · 2019-06-25 04:17:34

53

Views

Is the sequence $s_j = \sum_{k=0}^{k=j}e^{ik^2}$ bounded?

Published on 25 Jun 2019 - 4:17

score 44 · Answer 15 · 2026-04-05 18:37:47

44

Views

fractional imaginary calculation

Published on 05 Apr 2026 - 18:37

List Question

Show that $\left| z + \sqrt{z^2 + c^2} \right| > c$ for $\operatorname{Re}(z) > 0$

Find every $a \in \mathbb{R}$ such that $f = X^{2n+1} - (2n+1)X + a$ has a repeated root

Using roots of unity to find exact trig values

Ordering Complex Numbers

Find the complex square root of $7+6\sqrt2i$

Let $w \in G_{24}$ be a primitive root. Find every $n \in \mathbb{N}$ such that $w^{15n} + \sum^{11}_{i=1} \overline{w}^{2i+6}$ is purely imaginary.

How to solve for imaginary roots of a quartic that cannot be factored and has no real roots?

Complex number confussion

What is $\sqrt [3]{-1}$ and how does one obtain its value?

Let $w\in G_{18}$ be a primitive root of unity. Prove that $w^{16} \sum_{j=1}^{17}(w^3 \overline{w})^{3j+1}$ is imaginary pure.

How to find this complex logarithm value without using a calculator?

Can constants be complex for integral table?

Find the polar representation of $z = \sin\theta+i(1+\cos\theta)$

Is the sequence $s_j = \sum_{k=0}^{k=j}e^{ik^2}$ bounded?

fractional imaginary calculation

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