Complex Analysis Answers

3. Use De Moivre’s Theorem to determine the cube root of Z and leave your answer in polar

form with the angle in radians

(a) Z = 1+i√3

3. Let Z = i

(i) Write Z in a polar form (2)

(ii) Use De Moivre’s Theorem to determine Z4

Let f(z)=1/z^5 . Use the polar form of the Cauchy Riemann equations to determine where f is differentiable

suppose f(z) =1/z. write f in the form f(z) = u(x,y) + iv(x,y), where z = x+iy and u and v are real-valued functions

Let A ={ z E C : Im (z+2/z-2)≥ 1}.

(a) Sketch the set A in the complex plane.

(b) Is z = −2i a boundary point of A? Provide reasons for your answer.

(c) Is this set open, closed, both or neither? Provide reasons for your answer.

Let Z = i

(i) Write Z in a polar form

(ii) Use De Moivre’s Theorem to determine Z^4

Use De Moivre’s Theorem to determine the cube root of Z and leave your answer in polar

form with the angle in radians

(a) Z = 1+i√3