First Principles AI

Accedmychevron_right11thchevron_rightmathchevron_rightComplex Numberschevron_rightExercise 1.5

(i) $4+3i$

r=|z|=\sqrt{4^2+3^2}=5

Since $x>0$ and $y>0$ , $\theta$ lies in Quadrant I:

\theta=\tan^{-1}\left(\frac{3}{4}\right)

\boxed{4+3i=5\left(\cos\left(\tan^{-1}\frac{3}{4}\right)+i\sin\left(\tan^{-1}\frac{3}{4}\right)\right)}