Exponential form of complex numbers
Définition :
We denote by
the complex number of modulus
equal to
If the complex number
is of modulus
and of argument
we have:
With this notation, the calcultation rules become:
If
Assuming
non zero,
Remarque :
The algebraic form of complex numbers is more adapted to calculations of sums and substractions, whereas the trigonometric and exponential forms are more adapted to calculations of multiplications and divisions.
Fondamental : Euler's formulas
Fondamental :
Definition
root of a complex number.
We call
root of the complex number
any complex number
' such that
Theorem
The non zero complex number
admits
roots, given by:
