Question: Consider the complex numbers z1 = 4 + 4i, z2 = 6cis(11/6), and z3 = 18 6i. (a) Calculate the following complex numbers. All answers

Consider the complex numbers z1 = 4 + 4i, z2 = 6cis(11/6), and z3 = 18 6i.

(a) Calculate the following complex numbers. All answers that are in polar form must have a positive modulus and be in terms of the principal argument.

i. z1 in polar form.

ii. z2/|z2| in Cartesian form.

iii. z1z2 in polar form.

iv. z2/z1 in polar form.

v. (z1)-2 in Cartesian form.

vi. All complex numbers w that satisfies w3 = z2 in polar form.

(b) On an Argand diagram, sketch the subset S of the complex plane defined by S = {z C : |z z3| |z|, Arg(z) Arg(Z3)

Justify your answer

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