Complex Numbers - Cool math Algebra Help Lessons

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Coolmath Algebra
Complex Numbers Lesson 3 - The Quadratic Formula (page 2 of 2)
---- This algebra lesson explains how to use the quadratic formula when you get complex solutions.

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Now, try solving this guy:

WAY 1: FACTOR

WAY 2: SQUARE ROOT TRICK

x^2 + 25 = 0 gives ( x - 5i ) ( x + 5i ) = 0 which gives x - 5i = 0 or x + 5i = 0 which gives x = 5i or x = -5i

x^2 + 25 = 0 gives x^2 = -25 which gives sqrt( x^2 ) = +/- sqrt( -25 ) which gives x = +/- 5i

Your turn... and do it both ways:

Solve

Hey, have you noticed something interesting with all our answers?

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

{ -5i , 5i }
Look at this last guy in his official complex form:

Each of these answers is a pair -- one with a minus and one with a plus. Like

These are called complex conjugates. For example, the conjugate of

-5 + 3i is -5 - 3i ... the first one is plus is the second is minus

When you are solving quadratic equations, each complex solution will ALWAYS have his conjugate buddy with him!

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