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Complex Zeros

Solve  x^2 + 4 = 0

Let's use the square root trick!

x^2 = -4 gives sqrt( x^2 ) = +/- sqrt( -4 ) which gives x = +/- 2i

{ -2i , 2i }

When we are graphing these things do not show up on the graph!

But, hey...  when we set something = 0 like

x^2 + 4 = 0

isn't that how we find zeros?  YEP!

These things we just found are complex zeros (versus real zeros that we were finding before.)

So, here's the official scoop on complex zeros:

Complex zeros always occur
in conjugate pairs
a - bi and a + bi

 

Complex zeros do not show up on graphs!