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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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

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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