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# Complex Numbers to Solve Equations

By making use of the imaginary number i we can solve equations that involve the square roots of negative numbers.

Complex numbers enable us to solve equations that we wouldn't be able to otherwise solve. Examine the following example:

$x^2 = -11 \\ x = \sqrt{ \red - 11} \\ \sqrt{ 11 \cdot \red - 1} = \sqrt{11} \cdot i \\ i \sqrt{11}$

Without the ability to take the square root of a negative number we would not be able to solve these kinds of problems.