Question

Find the modulus and the amplitude of the complex number $1-i$.

Answer 1

Let $z=1-i$.

Now $|z|=\sqrt{1^2+(-1{)}^2}=\sqrt{2}$.

Since the point lies on the fourth quadrant then the amplitude of the complex number $z$ is $-{\tan }^{-1}\left|\frac{-1}{1}\right|=-\frac{\pi }{4}$.