First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(ii) $1+i$

r=|z|=\sqrt{1^2+1^2}=\sqrt{2}

Since $x>0$ and $y>0$ , $\theta=\frac{\pi}{4}$ .

\boxed{1+i=\sqrt{2}\left(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\right)}