Michael J. answered • 01/13/16

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Applying SImple Math to Everyday Life Activities

Conjugates have the plus/minus signs. Recall the solution when using the quadratic formula to solve a quadratic equation.

For this one, we use the fact that i

^{2}=-1First, work the first part of the proof.

(a + bi)(c + di) = ac + adi + bci + bdi

^{2} = (ac - bd) + (ad + bc)i

*This is the product of the numbers. Now take the conjugate of this product.*

**(ac - bd) - (ad + bc)i**

Now, we work the second part of the proof. Take the product of the conjugates.

(a - bi)(c - di) = ac - adi - bci + bdi

^{2} =

**(ac - bd) - (ad + bc)i**The two bolded results from both parts are the same.