Prove the complex Inequality $|z_1 + z_2| \le |z_1| + |z_2|$.

Asked Nov 26 '17 at 09:43

Active Nov 26 '17 at 09:52

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I have to be prove the following inequality, where $z_1$ and $z_2$ are two complex numbers. $$|z_1 + z_2| \le |z_1| + |z_2|$$

I know I can substitute Z as 'x + iy' and open both sides but I am confused about the inequality. Any help would be appreciated.

edited Nov 26 '17 at 09:52

Nosrati

asked Nov 26 '17 at 09:43

Talal Zahid

This inequality is equivalent to the geometric triangle inequality, because $|z| = \sqrt{x^2 + y^2}$ where $x = \mathrm{Re}, z, y = \mathrm{Im},z$. – jokersobak Nov 26 '17 at 09:49
1

you can square the whole inequality – Dr. Sonnhard Graubner Nov 26 '17 at 11:06

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