Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi.) (1 − i)^18

Answer 1

z = 1 - i

||z|| = √2

θ = π / 4

z¹⁸ = (√2)¹⁸(cos (π/4)(18) + i sin (π/4)(18))

You to simplify and answer.

Answer 2

(1-i)^18

=- 512i

=( sqr(1+1))^18)(cisx)^18

=2^9(cis18x)

=16(32)cis18x

= 512(cis18x)

= 512(cos18(7pi/4) + isin18(7pi/4)

= 512(cos63pi/2 + isin63pi/2)

=512(cos-pi/2 + isin-pi/2)

= 512(0 -i)

= -512i

check the answer

(1-i)^2 = 1-2i+1=-2i

(-2i)^2 = -4

(-4)^2 = 16

16^2 = 256

256(1-i)^2 =256(-2i)=-512i

which is actually much easier to do than DeMoivre's Theorem