Equations of degree 2.
We solve the equation
where
are complex numbers and
.
We have:
Define
.
- If
, then
. The equation has a double solution, namely
.
-
, then
has two complex square roots; we denote them
and
. Thus:
.
The equation has two distinct complex solutions, namely:
and |
|
Example 1.6.1
Solve the equation
, where
is a complex unknown.
. Thus,
has two complex square roots, namely
and
. The solutions
and
of the equation are given by:
and |
|
Example 1.6.2
Solve the equation
, where
is a complex unknown.
. The complex square roots of
are
and
(You can compute them either by the algebraic method, described in
subsection 5.3,
or by the trigonometric method, described in subsection 5.1).
The solutions
and
of the equation are given by:
and
 |
|
![$\displaystyle \forall z \in \mathbb{C}, az^2+bz+c = a \left[ \left( z+ \frac {b}{2a} \right) ^2 + \frac {b^2-4ac}{4a^2} \right]$](/images/maths/complex-analysis/degree/img338.png)
