# Equations of degree 2.

We solve the equation

where are complex numbers and .

We have:

Define .

1. If , then . The equation has a double solution, namely .
2. , 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

Noah Dana-Picard 2007-12-24