Convert the given complex number in polar form 1 - i and evaluate

The complex number is 1-i

Let \( rcos\theta=1\) and \( rsin\theta=-1\)

squaring and adding

\( r^2cos^2\theta+r^2sin^2\theta=1^2+(-1)^2\)

\( r^2(cos^2\theta+r^2sin^2\theta)=1+1\)

r² = 2

\( r=\sqrt{2}\)

\( \sqrt{2}cos\theta=1\) and  \( \sqrt{2}sin\theta=-1\) 

\(cos\theta=\dfrac{1}{\sqrt{2}}\) and \( sin\theta=-\dfrac{1}{\sqrt{2}}\)

\(\theta=-\dfrac{\pi}{4}\) [ As θ liesin the IV quadrant ]

1- i = rcosθ + irsinθ

= \(\sqrt{2}cos(-\dfrac{\pi}{4})+i\sqrt{2}sin(-\dfrac{\pi}{4})\)

\(\sqrt{2}[cos(-\dfrac{\pi}{4})+isin(-\dfrac{\pi}{4})]\)