Question

Find the modulus and principal amplitude of $-4$

Answer 1

Let $z=-4+0i$.

Then, modulus of $z=|z|=\sqrt{(-4{)}^2+0^2}=\sqrt{16}=4$.

Clearly, the point in the $z-plane$ the point $z=-4+0i=(-4,0)$ lies on the negative side of real axis.

Therefore, the principle amplitude of $z$ is $\pi$.