Complex Solutions of Quadratic Equations
When using the Quadratic Formula to solve a quadratic equation, you often obtain a
result such as
 which you know is not a real number. By factoring out
 you can write this number in standard form.
The number
 is called the principal square root of
-3.
Principal Square Root of a Negative Number
If a is a positive number, the principal square root of the negative number
-a
is
STUDY TIP
The definition of principal
square root uses the rule
 for
a > 0 and b < 0. The rule is not
valid if both a and b are negative.
For example,
whereas
To avoid problems with multiplying
square roots of negative numbers, be
sure to convert to standard form before
multiplying.
Example 1
Writing Complex Numbers in Standard Form
Example 2
Complex Solutions of a Quadratic Equation
Solve 3x2 - 2x + 5 = 0.
Solution
| x |
 |
Quadratic Formula
|
| |
 |
Simplify.
|
| |
 |
Write in i-form. |
| |
 |
Standard form |
|
