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QUESTION

If $\theta$ is the real number between 0 and $\pi/2$ such that
$\tan\theta=4/3$ find the real and imaginary parts of the complex
number $(3+4i)^{3+4i}$, expressing your answer in terms of
$\theta$.



ANSWER

Real part is $\sin 1\cosh 1$, Imaginary part is $\cos 1\sinh 1$.

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