Question: ANSWER THIS QUESTIONS IN DETAIL 2. (a) Evaluate the complex function f(z) = rsin 30 + i cos 20 at the point z = 1

ANSWER THIS QUESTIONS IN DETAIL

2. (a) Evaluate the complex function f(z) = rsin 30 + i cos 20 at the point z = 1 + i. (b) Find the real and imaginary parts u and v of the given complex function f(z) = z + = as functions of / and 0. Z (c) Find the images of the rectangle with vertices -2 + 3i, 2 + 3i, -5 + 7i and 5 + 7i under the linear mapping f(z) = 6iz + 4 + 3i Z' (d) Find Limz--1 2+1 .3-1 |z| # 1 (e) Show that the function f (z) = 22+2+1 -1+1v3 is continuous at the point |z| = 1 2 1+1v3 Zo 2 (4+4+3+4+5)

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