show a modulus

**hurz** · July 1st 2011, 01:25 PM

How to show that
$|\exp(\frac{-x}{a+b i})| = \exp(\frac{ax}{a^2+b^2})$

where x, a and b are real and i is the complex unit and | | means the modulus

**Plato** · July 1st 2011, 01:49 PM

Originally Posted by hurz

How to show that
$|\exp(\frac{-x}{a+b i})| = \exp(\frac{ax}{a^2+b^2})$

Do you know that $\left| {\exp \left( z \right)} \right| = \exp \left( {\text{Re} (z)} \right)~?$

Do you know that $\frac{{ - x}}{{a + bi}} = \frac{{ - ax + bxi}}{{a^2 + b^2 }}~?$

Now as it stands you have a sign error in what you posted.

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