Splitting an exponential complex number into real and imaginary parts

[dan5]

e^-z2

where z is a complex number a+ib

 

[I like Serena]

Welcome to PF, dan5!

Can you calculate -z²?

-z² should be of the form c + id.

According to Euler's formula, we have $e^{c+id} = e^c ( \cos d + i \sin d )$.
So the real part is $e^c \cos d$ and the imaginary part is $e^c \sin d$.

 

[dan5]

Ahhh now I see, thanks to you, and to Euler!