Question

Express $1-i$ in modulus-amplitude form.

Answer 1

Let $z=1-i$

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

and $\theta ={\tan }^{-1}\left(\frac{-1}{1}\right)=\frac{-\pi }{4}$

Thus modulus-amplitude form is,

$z=|z|(\cos \theta +i\sin \theta )=\sqrt{2}(\cos \frac{-\pi }{4}+i\sin \frac{-\pi }{4})$