Question

Find the amplitude of $i(1+i)$.

Answer 1

Let $z=i(1+i)$

or, $z=i-1$

or, $z=-1+i$.

So it is clear that the point $z$ lies on the second quadrant.

Therefor the amplitude of the complex number represented by $z$ is

$=\pi -{\tan }^{-1}\left|\frac{1}{-1}\right|=\pi -{\tan }^{-1}1=\pi -\frac{\pi }{4}=\frac{3\pi }{4}$.