How do we use complex conjugate to divide imaginary numbers?

How do we use complex conjugate to divide imaginary numbers?

To divide imaginary numbers you write the quotient as a fraction and divide the numerator and the denominator  by the conjugate of the denominator. 

The complex conjugate of (a+bi) is (a-bi)

* Note you just change the sign in the middle. 

Example:

(1-2i)/ (3+i)

-First, find the complex conjugate of the denominator 

-Complex conjugate of (3+i) is (3-i)

-Next multiply both numerator and denominator by (3-i)

-If you foil (1-2i) and (3-i) you get 1-7i

-If you foil (3+i) and (3-i) you get 10

-Your final; answer is 1-7i/10

    

*Note i x i= i^2= -1

How to foil?

Citation (images):- http://literacy.kent.edu/Oasis/Resc/Educ/algebra.html

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