Complex numbers

Complex Numbers

Keywords:

z=a+ib  ;  a, b, i=-1

The modulus of a complex number

r=a2+b2

The argument of a complex number

tg φ=ba (a0)

The real part of the complex number

Rez=a=r·cos φ

The imaginary part of the complex number

Imz=b=r·sin φ

Rectangular form of a complex number

z=a+ib

Polar form of a complex number

z=r·cos φ+i·sin φ

Exponential form of a complex number

z=r·eφi

Conjugate of a complex number

z=a+ib=r·cos φ+i·sin φ=r·eφi
z¯=a-ib=r·cos φ-i·sin φ=r·e-φi