A complex number $z$ satisfies $z^3=-2+11i$. Use conjugate properties without finding $z$. Fin

Question

A complex number $z$ satisfies $z^3=-2+11i$. Use conjugate properties without finding $z$. Find $(z^*)^3$.[1] Find $z^3+(z^*)^3$.[1] Find $(z^*)^6$ in Cartesian form.[2]

Accepted Answer

(a) $-2-11i$ (b) $-4$ (c) $-117+44i$

Using conjugates of powers

Using conjugates of powers

Solution:

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