Reminder on complex numbers

Form of a complex number

A complex number I can be written in different forms:

• in Cartesian form:

  I = Ir + j Ii

  where:

  Ir : real part of I

  Ii : imaginary part of I

  j: pure imaginary number with j² = –1

• in Polar form (or exponential form):

  $I=Imod e^{j\varphi }$

  where:

  I mod : modulus of I

  ϕ : argument of I (or phase)

  j: pure imaginary number with j² = –1

Conjugate of a complex number

The conjugate of I is defined by:

I* = Ir – j Ii

Modulus of a complex number

The modulus of I is defined by: