Question 1 (a) Suppose that z = x + yi and f(z) = x² – y? – 2y + (2x – 2xy)i. Use the expressions - 1 x = (z + z) and y = 2 1 :(z - 2) to write f (2) in terms of z, and simplify the result. 2i (b) If...

Extracted text: Question 1 (a) Suppose that z = x + yi and f(z) = x² – y? – 2y + (2x – 2xy)i. Use the expressions - 1 x = (z + z) and y = 2 1 :(z - 2) to write f (2) in terms of z, and simplify the result. 2i (b) If z = x + iy and the function f(2) = u(x, y) + iv(x, y) is defined by f(2) = z2 + z + 1, find u(x, y) and v(x, y) as the functions of x, y and show that u(x, y) and v(x, y) satisfies the Cauchy-Riemann equation throughout the whole complex z-plane..