what are the indicated powers of these complex numbers:
a. (2 – 3i )^2
b. (3 + 4i )^3
c. [2 cis(300°)]^5
d. ( cos (4pi/3) + i sin (4pi/3)) ^4

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  1. a. just square it
    (2 - 3i)^2
    = 4 - 12i + 9i^2
    = 4 - 12i - 9
    = -5 - 12i

    De Moivre's theorem for the others, I will do c.

    c. [2 cis(300°)]^5
    = 2^5 cis 1500° , dividing out multiples of 360, keeping the remaining angle
    = 32cis60°
    or 32(cos60 + i sin60)
    = 32(√3/2 + i (1/2) )
    = 16√3 + 16i

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