8. a) Write the complex number -2 -2in trigonometry form. Be sure to graph when looking...

Question

Question

Answer 1

Answer #1

a)

- 2 - 2i

r = sqrt [ x^2 + y^2 ]

r= sqrt [ -2^2 + - 2^2 ]

r = 2 sqrt 2

Theta = tan^-1 ( - 2/-2) = pi/4

Trigonometric form is

b)

( - 2 - 2i )^8

= (2 sqrt 2)^8 ( cos 8 pi/4 + i sin 8pi/4 )

4096 ( 1 )

= 4096

(-2-2i)^8 = 4096

Answer 2

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