3. Show that f'(z) exists everywhere, and compute f'(z) when (a) f(z) = iz + 2,...

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3. Show that f'(z) exists everywhere, and compute f'(z) when (a) f(z) = iz + 2, (b) f(2)=ee, (c) f(2)= 2³; (d) f(z) = cos r cosh y – i sin r sinh y. Hint: Recall that and sinhy=,e”. 2 4. Show that f(z) = 2xy + i(x² - y²) is nowhere analytic. cosh y = e" + ey 2 3. Show that f'(z) exists everywhere, and compute f'(z) when (a) f(z) = iz + 2, (b) f(2)=ee, (c) f(2)= 2³; (d) f(z) = cos r cosh y – i sin r sinh y. Hint: Recall that and sinhy=,e”. 2 4. Show that f(z) = 2xy + i(x² - y²) is nowhere analytic. cosh y = e" + ey 2

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