Question

Write 4sqrt(3i)-4 in polar form. Find values r>0 and theta is between 0 and 2pi

Answer 1

I'm not sure about this, so you will have to double check, but
\[r = \sqrt{a^2+b^2}=\sqrt{4^2+(4\sqrt{(3)})^2}=8\]
And the angle is
\[\theta = \tan^{-1} (\frac{4\sqrt3}{-4}) = - \frac{\pi}{3}\]
This is the same as 2pi/3 or 120 degrees