Question

Write the number in polar form with argument between 0 and 2π. −8 + 8i

Answer 1

To write from the complex to polar coordinates w proceed as follows:
Let Z=-8+8i
lZl=√(-8)²+8²=√128=8√2
Argument: θ is in second quadrant
∴ θ=π-arctan(8/8)=π-π/4=(3π)/4
∴ Z=-8+8i
=8√2[cos(3π)/4+isin(3π)/4]