Question 642901
express ( -1 + root(3)i)^10 in a+bi form
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{{{(-1 + sqrt(3)i)^10}}}
is in a + bi form, with the exponent.
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If you want to simplify it some:
magnitude (z) = {{{sqrt(1 + 3) = 2}}}
---> 2cis(atan(-sqrt(3))
z = 2cis(300)
z^10 = 2^10cis(3000)
= 1024cis(120)
= 1024cos(120) + 1024i*sin(120)
= {{{-512 + 512sqrt(3)i}}}