Splitting an exponential complex number into real and imaginary parts

AI Thread Summary
The discussion focuses on splitting the exponential of a complex number, specifically e^(-z^2), where z is defined as a + ib. Participants clarify that -z^2 can be expressed in the form c + id. They reference Euler's formula, which states that e^(c+id) equals e^c multiplied by (cos d + i sin d). This leads to the conclusion that the real part is e^c cos d and the imaginary part is e^c sin d. The exchange highlights the application of Euler's formula in understanding complex exponentials.
dan5
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e-z2

where z is a complex number a+ib
 
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Welcome to PF, dan5! :smile:

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

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