# Complex Numbers

Keywords:

The modulus of a complex number

$r=\sqrt{{a}^{2}+{b}^{2}}$

The argument of a complex number

$tg\phi =\frac{b}{a}\left(a\ne 0\right)$

The real part of the complex number

The imaginary part of the complex number

Rectangular form of a complex number

$z=a+ib$

Polar form of a complex number

$z=r·\left(\mathrm{cos}\phi +i·\mathrm{sin}\phi \right)$

Exponential form of a complex number

$z=r·{e}^{\phi i}$

Conjugate of a complex number

$z=a+ib=r·\left(\mathrm{cos}\phi +i·\mathrm{sin}\phi \right)=r·{e}^{\phi i}$
$\overline{z}=a-ib=r·\left(\mathrm{cos}\phi -i·\mathrm{sin}\phi \right)=r·{e}^{-\phi i}$