Rewrite the complex number in polar form

Question

z= r(cos(theta) + i sin (theta))

z =2 - 2i = ?

Answer 1

Lets solve this shall we ?

So, we must convert the given complex number into polar form representing r(cosθ + isinθ). First, we must find r such that

r² = a² + b², where a = 2 and b = -2. Then

r² = (2)² + (-2)²

r² = 4 + 4

r² = 8

r = 2√2 = 2.83 (rounded to the nearest hundredth)

and let cosθ = a/r and sinθ = b/r where cosθ = 2/(2√2) = √2/2 and sinθ = 2/(2√2) = -√2 / 2.

Since a > 0, we must use θ = tan^-1(b/a) = tan^-1(-2/2) = -0.79 (in radians)

Thus, 2-2i in polar form is 2.83(cos(-0.79) + isin(-0.79))

I hope this helped!