Polar Form

For a given complex number in the form: $z=a+bi$ $z=r{e}^{i\theta }$ Where:

• $r=|z|$ (See Complex Number Modulus)
• $\cos \theta =\frac{a}{r}$
• $\sin \theta =\frac{b}{r}$
• $\theta$ is considered the argument

Polar Form Conjugate

$\overline{z}=\overline{r(\cos \theta +i\sin \theta )}=r{e}^{-i\theta }$

Specific Polar Forms You Should Remember

• $e^{i2\pi }=1$
• $e^{i\frac{\pi }{2}}=i$
• $e^{i\pi }=-1$
• $e^{i\frac{3\pi }{2}}=-i$

Concepts

• De Moivre’s Theorem
• Multiplying Numbers in Polar Form