AMC 12B 2024 (Problem 12)

Suppose

z

is a complex number with positive imaginary part, with real part greater than

1

, and with

|z|=2

. In the complex plane, the four points

0

z

z^2

, and

z^3

are the vertices of a quadrilateral with area

15

. What is the imaginary part of

z

\text{(A)}\;\frac{3}{4}

\text{(B)}\;1

\text{(C)}\;\frac{4}{3}

\text{(D)}\;\frac{3}{2}

\text{(E)}\;\frac{5}{3}