Question

Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $

score 167 · Answer 1 · 2026-04-13 20:53:19

167

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Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $

Published on 13 Apr 2026 - 20:53

score 112 · Answer 2 · 2014-05-01 00:43:38

112

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score 188 · Answer 3 · 2026-04-09 09:18:54

188

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score 124 · Answer 9 · 2026-04-11 17:42:28

124

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Published on 11 Apr 2026 - 17:42

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695

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204

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62

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score 1k · Answer 15 · 2026-04-08 17:54:59

1k

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List Question

Suppose $z \neq -1$ is a complex number of norm 1. Prove that $(\frac{1+z}{|1+z|})^2 =z $

Show that $(x-\alpha)(x-\overline{\alpha})$ is a also a factor of $p(t)$ over the complex numbers

Proving a simple equation with complex numbers

Find all complex numbers z such that $\Im(-z+i) = (z+i)^2$

Finding the least value for points in a locus

Why does the Mandelbrot shape show up in other fractals?

About gaussian integers and orders.

locus of a complex number in the form |z-a|=k|z-b|

Explain why there are two complex numbers z such that $|z| = 1$ and that satisfy the equation $|z| = |z-1|.$

Laurent Series of $f(z) = \frac{1}{e^z - 1}$

How to show $\displaystyle\lim_{n\to\infty}\sqrt[n]{|z^n|}=|z|$

Convert complex logarithms to inverse tangents

Is there infinitely many "complex units"

Proof using complex numbers

How to expand out negative powers for complex numbers

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