Question

Write the amplitude and modulus of $-4-4i$.

Answer 1

Modulus of $-4-4i$ is $\sqrt{4^2+4^2}=\sqrt{32}=4\sqrt{2}$.

The point represented by the complex number lies in the third quadrant.

Now amplitude of the given complex number, is $-\pi +{\tan }^{-1}\left|\frac{-4}{-4}\right|=-\frac{3\pi }{4}$.