Let z = 2 i and = 1 i . For the first four subquestions (A to D), you need to have z^

Let z=2i and α=1−i. For the first four subquestions (A to D), you need to have z^α. Remember that whenever you evaluate z^α, at that time, work with the principle value only. The last subquestion (E) is a problem dealing with single-valued functions.

A. Which of the following is true? |20 xp ((1 i) (In 2 +i 3) |z = i exp (In 4) |cos (In 2 4) i sin (In 2 )] - za = exp ((1 i) Log 2i) Oza = exp (In 2 + 5) [cos (In 2 ) i sin (In 2 5)] - za - 5.9054 + 9.7505 i B. If za = f (z), then evaluate Re (f (z)) + Im (f (z)). C. If za = w then what is the value of Im (w) Re (w) ?