Question

To prove that $\frac{|x-y|}{\sqrt{1+|x|^2}+\sqrt{1+|y|^2}}$ is a metric on $\mathbb{C}$

score 71 · Answer 1 · 2026-04-11 18:35:36

71

Views

To prove that $\frac{|x-y|}{\sqrt{1+|x|^2}+\sqrt{1+|y|^2}}$ is a metric on $\mathbb{C}$

Published on 11 Apr 2026 - 18:35

score 129 · Answer 2 · 2026-04-11 22:12:22

129

Views

Power of Complex Numbers in Contest Geometry

Published on 11 Apr 2026 - 22:12

score 87 · Answer 3 · 2019-09-09 16:15:09

87

Views

Show that $\frac{1}{2}(|z|+|w|)|\frac{z}{|z|} + \frac{w}{|w|}| \le |z+w|$ with $z \neq 0$ and $w\neq0$

Published on 09 Sep 2019 - 16:15

score 60 · Answer 4 · 2019-09-09 16:50:56

60

Views

2.17.32 - Mary L Boas.

Published on 09 Sep 2019 - 16:50

score 31 · Answer 5 · 2026-04-10 02:18:40

31

Views

determining complex numbers, knowing the results of the equation

Published on 10 Apr 2026 - 2:18

score 501 · Answer 6 · 2026-03-28 03:52:52

501

Views

To prove that $\mathbb{Q}$ is the smallest subfield of $\mathbb{C}$

Published on 28 Mar 2026 - 3:52

score 173 · Answer 7 · 2026-04-09 16:44:50

173

Views

How to solve a complex exponential functional equation which contains the multivalued argument function of complex numbers

Published on 09 Apr 2026 - 16:44

score 77 · Answer 8 · 2026-04-09 14:32:18

77

Views

Evaluating $\frac{\sum_{k=1}^{1010} i^{2k-1}}{\prod_{k=1}^{1010} i^{2k}}$, where $i$ is the imaginary unit

Published on 09 Apr 2026 - 14:32

score 196 · Answer 9 · 2019-09-11 09:29:17

196

Views

Infinitely Many Zeros

Published on 11 Sep 2019 - 9:29

score 42 · Answer 10 · 2026-03-25 09:47:12

42

Views

which domain does this Möbius map to $\Re(w) > 0$?

Published on 25 Mar 2026 - 9:47

score 1.7k · Answer 11 · 2019-09-11 12:45:27

1.7k

Views

In showing the principal branch of $\operatorname{Log}(z)$ is holomorphic on $\Bbb C\smallsetminus \mathbb{R}^{\leq 0}$, where is the branch used?

Published on 11 Sep 2019 - 12:45

score 598 · Answer 12 · 2019-09-12 18:09:16

598

Views

Imaginary part of the following complex number.

Published on 12 Sep 2019 - 18:09

score 326 · Answer 13 · 2026-03-26 17:52:35

326

Views

Finding all the complex roots of $x^3 - x^2 + 1 = 0$

Published on 26 Mar 2026 - 17:52

score 4.7k · Answer 14 · 2026-03-27 20:19:51

4.7k

Views

Showing whether a matrix is diagonalizable over $C$?

Published on 27 Mar 2026 - 20:19

score 439 · Answer 15 · 2026-03-30 10:16:08

439

Views

What is the graphical representation of complex roots on the real Cartesian plane?

Published on 30 Mar 2026 - 10:16

List Question

To prove that $\frac{|x-y|}{\sqrt{1+|x|^2}+\sqrt{1+|y|^2}}$ is a metric on $\mathbb{C}$

Power of Complex Numbers in Contest Geometry

Show that $\frac{1}{2}(|z|+|w|)|\frac{z}{|z|} + \frac{w}{|w|}| \le |z+w|$ with $z \neq 0$ and $w\neq0$

2.17.32 - Mary L Boas.

determining complex numbers, knowing the results of the equation

To prove that $\mathbb{Q}$ is the smallest subfield of $\mathbb{C}$

How to solve a complex exponential functional equation which contains the multivalued argument function of complex numbers

Evaluating $\frac{\sum_{k=1}^{1010} i^{2k-1}}{\prod_{k=1}^{1010} i^{2k}}$, where $i$ is the imaginary unit

Infinitely Many Zeros

which domain does this Möbius map to $\Re(w) > 0$?

In showing the principal branch of $\operatorname{Log}(z)$ is holomorphic on $\Bbb C\smallsetminus \mathbb{R}^{\leq 0}$, where is the branch used?

Imaginary part of the following complex number.

Finding all the complex roots of $x^3 - x^2 + 1 = 0$

Showing whether a matrix is diagonalizable over $C$?

What is the graphical representation of complex roots on the real Cartesian plane?

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