Writing Complex Numbers in Polar Form (Leaving Cert Mathematics): Flashcards

Magnitude (modulus) and angle (argument) in the plane.

$z=r(\cos\theta+i \sin\theta)$, where $r$ is the modulus.

$r=|z|=\sqrt{a^2+b^2}$ for $z=a+bi$.

$\theta=\tan^{-1}(|b|/|a|)$ for $z=a+bi$.

$z=\sqrt{13}(\cos 0.983+i \sin 0.983)$.

$r=\sqrt{9+3}=\sqrt{12}=2\sqrt{3}$.

$r = 2$, the modulus of the complex number.

Modulus is $\sqrt{9 + 3} = \sqrt{12} = 2\sqrt{3}$.

Depends on quadrant; specific calculations needed.

$\theta=180°-A$ or $\theta=\pi-A$ in radians.