Question

Write the complex number in polar form with argument θ between 0 and 2π.

−9πi

Answer 1

r=+sqrt(a^2+b^2)=+sqrt(0^2+(-9\pi)^2=9\pi
tan theta=b/a=inf
theta=\pi/2
Polar form is:
9\pi(cos\pi/2+i*sin\pi/2)

Answer 2

Sorry. Have to make a correction:
tan theta=b/a=(-9pi)/0=-(infinity)
theta=(3*pi)/2
Polar form is:
9*pi(cos((3*pi)/2) + i*sin((3*pi)/2))