Write the complex number z=-2+2i in trigonometric form.

Answer 1

we want r(cos T + i sin T)
r = sqrt ((-2)^2 +2^2) =sqrt 8
=2 sqrt2

-2 = r cos T = 2 sqrt 2 cos T
cos T =-sqrt 2 / 2
T = 3 pi/4

2 = R sin T = 2 sqrt 2 sin T
sin T = sqrt2 /2
T = 3 pi/4 all right
so
z =2 sqrt 2[cos .75 pi+isin .75 pi]