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Multiplying Complex Numbers

To multiply two complex numbers , use the FOIL method for multiplying binomials , and remember that i 2 = − 1 .

Example:

Multiply the two complex numbers 3 + 5 i and 2 + 4 i .

( 3 + 5 i ) ( 2 + 4 i ) = ( 3 ) ( 2 ) + ( 3 ) ( 4 i ) + ( 5 i ) ( 2 ) + ( 5 i ) ( 4 i )                                                                 = 6 + 12 i + 10 i + 20 i 2                                                                 = 6 + 22 i + 20 ( − 1 )                                                                 = − 14 + 22 i

The product is − 14 + 22 i .