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
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