Question

Inequality $\lvert(1+\lvert u\rvert^2) v-(1+\lvert v\rvert^2)u\rvert > \lvert u\bar{v}-\bar{u}v\rvert$ for complex $u,v$

score 131 · Answer 1 · 2018-09-04 12:06:25

131

Views

Inequality $\lvert(1+\lvert u\rvert^2) v-(1+\lvert v\rvert^2)u\rvert > \lvert u\bar{v}-\bar{u}v\rvert$ for complex $u,v$

Published on 04 Sep 2018 - 12:06

score 182 · Answer 2 · 2018-09-04 12:15:11

182

Views

Show that $(a-b)(c-d)(\bar{a}-\bar{d})(\bar{c}-\bar{b})+i(c\bar{c}-d\bar{d})\text{Im}(c\bar{b}-c\bar{a}-a\bar{b})$ is real

Published on 04 Sep 2018 - 12:15

score 506 · Answer 3 · 2026-03-30 07:09:12

506

Views

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Published on 30 Mar 2026 - 7:09

score 44 · Answer 4 · 2018-09-04 16:53:06

44

Views

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score 45 · Answer 5 · 2018-09-04 20:17:37

45

Views

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score 711 · Answer 6 · 2018-09-04 21:07:43

711

Views

compute $(\sqrt 3 + i)^{14} + ( \sqrt 3 - i)^{14}$

Published on 04 Sep 2018 - 21:07

score 49 · Answer 7 · 2018-09-05 00:13:50

49

Views

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Published on 05 Sep 2018 - 0:13

score 5.1k · Answer 8 · 2018-09-05 04:01:41

5.1k

Views

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Published on 05 Sep 2018 - 4:01

score 653 · Answer 9 · 2018-09-05 05:49:13

653

Views

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Published on 05 Sep 2018 - 5:49

score 131 · Answer 10 · 2018-09-05 18:34:46

131

Views

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Published on 05 Sep 2018 - 18:34

score 137 · Answer 11 · 2026-03-31 22:22:13

137

Views

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Published on 31 Mar 2026 - 22:22

score 66 · Answer 12 · 2018-09-06 07:15:52

66

Views

Find roots of $x^3-(2\sqrt 2+i)x^2 + (4+2i\sqrt 2)x-4i=0$ knowing that at least one of the roots is from the set $\{i, -i\}.$

Published on 06 Sep 2018 - 7:15

score 126 · Answer 13 · 2026-03-27 04:22:51

126

Views

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Published on 27 Mar 2026 - 4:22

score 246 · Answer 14 · 2026-03-24 22:10:50

246

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Published on 24 Mar 2026 - 22:10

score 46 · Answer 15 · 2018-09-06 11:10:35

46

Views

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Published on 06 Sep 2018 - 11:10

List Question

Inequality $\lvert(1+\lvert u\rvert^2) v-(1+\lvert v\rvert^2)u\rvert > \lvert u\bar{v}-\bar{u}v\rvert$ for complex $u,v$

Show that $(a-b)(c-d)(\bar{a}-\bar{d})(\bar{c}-\bar{b})+i(c\bar{c}-d\bar{d})\text{Im}(c\bar{b}-c\bar{a}-a\bar{b})$ is real

Are the imaginary units of complex numbers anyhow related to vectors?

Complex number problem using property

complex numbers equation deg 4

compute $(\sqrt 3 + i)^{14} + ( \sqrt 3 - i)^{14}$

Zeroes of a polynomial. Evaluate an expression

How to solve the equation $(z+1)^7 = z^7$ for all $z$?

Complex Numbers: Convert to rectangular form

Graph complex inequality $|1/z|<1$, when $z \in \mathbb{C}$

Finding remaining polynomial after finding complex factors

Find roots of $x^3-(2\sqrt 2+i)x^2 + (4+2i\sqrt 2)x-4i=0$ knowing that at least one of the roots is from the set $\{i, -i\}.$

Solve a complex equation with conjugate and square

Relation between dilogarithm and its complex conjugate

Solving a complex equation more efficiently

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