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There is one main place that complex numbers will pop up on you:

The Quadratic Formula!

Sometimes, you'll get negative numbers under that radical.

Here's an example:

Solve  x^2 - 6x + 25 = 0

x = 6 +/- sqrt( 36 - 4 ( 25 ) ) / 2 = 6 +/- sqrt( -64 ) / 2 = 6 +/- 8i / 2 ... which you can rewrite as 6/2 +/- 8i/2 = 3 +/- 4i

 

So, the solutions are 3 - 4i and 3 + 4i

Here's another one:

Solve  2x^2 + x+10= 0

x = -1 +/- sqrt( 1 - 4 ( 2 ) ( 25 ) ) / 4 = -1 +/- sqrt( -79 ) / 4 = -1 +/- sqrt( 79 ) i / 4

{ ( -1 - sqrt( 79 ) i ) / 4 , ( -1 + sqrt( 79 ) i ) / 4 }


YOUR TURN:

Solve 

x^2 - 10x + 9 = 0

4x^2 - x + 7 = 0