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How do I find a, b, c, d, f, and g so that they satisfy the following equations?

 

\(\begin{align*} e^{\pi i/2} &= a +bi, \\ e^{-2\pi i/3} &= c+di, \\ e^{9\pi i/4} &= f + gi. \end{align*}\)

 

I have no idea how to get started. Can someone provide an explanation of the steps? Thank you!

 Mar 2, 2024
 #1
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Here are the answers to your question:

 

e^(pi*i/2) = 1/2 + 1/2*i.

 

e^(-2*pi*i/3) = 1/sqrt(2) - 1/sqrt(3)*i

 

e^(9*pi*i/4) = 1/3 + sqrt(2)/4*i

 

Hope this helps!

 Mar 5, 2024

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