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Complex Conjugates

Every complex number has a complex conjugate. The complex conjugate of a + bi is a - bi. For example, the conjugate of 3 + 15i is 3 - 15i, and the conjugate of 5 - 6i is 5 + 6i.

When two complex conjugates a + bi and a - bi are added, the result is 2a. When two complex conjugates are subtracted, the result if 2bi. When two complex conjugates are multiplied, the result, as seen in Complex Numbers, is a2 + b2.

Dividing Complex Numbers

To find the quotient of two complex numbers, write the quotient as a fraction. Then multiply the numerator and the denominator by the conjugate of the denominator. Finally, simplify the expression:


=  
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Examples:

(3 + 2i)÷(4 + 6i) =?


 =  
 =  
 =  
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 =.  

(6 + 3i)÷(7 - 2i) =?


 =  
 =  
 =  
 =  
 =.  

(3 - i)÷(- 5 + i) =?


 =  
 =  
 =  
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 =.  

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