Write the complex number 6-6i in polar form with argument θ between 0 and 2π.

Answer 1

6-6i
magnitude = √(36 + 36) = √72 = 6√2
angle:
tanθ = -6/6 = -1 , where θ is in 4th quadrant of the Argand plane
θ = 315° or 7π/4 radians

6 - 6i = 6√2(cos(7π/4) + i sin(7π/4))
sometimes shortened to 6√2 cis (7π/4)