(a) Show that cos z = cos ¯z. (b) Is sin z = sin ¯z? (c) If f(z)=1+ iz, is f(z) = f(¯z)? (d) If f(z) is expanded in a power series with real coefficients, show that f(z) = f(¯z). (e) Using part (d), verify, without computing its value, that i[sinh(1 + i) − sinh(1 − i)] is real.

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