A Find 1i8 B Find the indicated roots and graph the roots in

A) Find: (1-i)^8

B) Find the indicated roots and graph the roots in the complex plane. The fifth roots of 32

Solution

Solution : (1-i)^8

a. r=|1-i | = 1+1 = 2.

tan (\\theta)= -1/1 =-1.

Thus theta = -/4

(1-i)^8 = (2)^8( cos 8(2n+/4)+i sin 8(2n+/4))

=16(cos 2(8n+)+i sin 2(8n+))

=16( cos (16n+2)+i sin (16n+2))

=16 (cos 16n + i sin 16n).

b. Substitute the value of n =0,1,2,...8.

For n=1

16(cos 16+i sin 16)

=16.

For n=4

16(cos 64+i sin 64)

=16