Establish the formulas cos(x + iy) = cos x cosh y - i sin x sinh y, sin(x + iy) = sin x cosh y + i cos x sinh y, where cosh u = 1/2(e^u + e^-u), u real sinh u = 1/2(e^u - e^-u), u real.
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Step 1: Recall Euler's formulas for complex exponentials: \[ e^{ix} = \cos x + i \sin x \] \[ e^{-ix} = \cos x - i \sin x \] Show more…
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