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There exist real numbers  such that

\begin{align*}
e^{\pi i/2} &= a +bi, \\
e^{-2\pi i/3} &= c+di, \\
e^{9\pi i/4} &= f + gi.
\end{align*}
Enter  a,b,c,d,f,g in that order.

Mar 21, 2022

You can write  $$e^{i\theta}=\cos \theta+i\sin \theta$$, so the real part of each number (a, c and f) is obtained using $$\cos \theta$$ and the imaginary part (b, d and g) using $$\sin \theta$$.