Complex numbers

# Complex Numbers

## Keywords:

 $r=\sqrt{{a}^{2}+{b}^{2}}$ The modulus of a complex number $tg\phi =\frac{b}{a}\left(a\ne 0\right)$ The argument of a complex number The real part of the complex number The imaginary part of the complex number

 $z=a+ib$ Rectangular form of a complex number $z=r·\left(\mathrm{cos}\phi +i·\mathrm{sin}\phi \right)$ Polar form of a complex number $z=r·{e}^{\phi i}$ Exponential form of a complex number $z=a+ib=r·\left(\mathrm{cos}\phi +i·\mathrm{sin}\phi \right)=r·{e}^{\phi i}$ $\overline{z}=a-ib=r·\left(\mathrm{cos}\phi -i·\mathrm{sin}\phi \right)=r·{e}^{-\phi i}$ Conjugate of a complex number