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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:

x^2 + 25 = 0

  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

{ -5i , 5i }

  

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

 

{ -5i , 5i }

Your turn...  and do it both ways:

Solve  x^2 + 81 = 0

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

{ 3 - 4i , 3 + 4i }

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

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

{ 0 - 5i , 0 + 5i }

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

{ a - bi , a + bi }

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!

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
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