How to show that $\displaystyle |\exp(\frac{-x}{a+b i})| = \exp(\frac{ax}{a^2+b^2})$ where x, a and b are real and i is the complex unit and | | means the modulus
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Originally Posted by hurz How to show that $\displaystyle |\exp(\frac{-x}{a+b i})| = \exp(\frac{ax}{a^2+b^2})$ Do you know that $\displaystyle \left| {\exp \left( z \right)} \right| = \exp \left( {\text{Re} (z)} \right)~?$ Do you know that $\displaystyle \frac{{ - x}}{{a + bi}} = \frac{{ - ax + bxi}}{{a^2 + b^2 }}~?$ Now as it stands you have a sign error in what you posted.
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