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Adding and Subtracting Complex Numbers

To add or subtract twocomplex numbers, simply add the real and imaginary parts separately.

Example 1:

Simplify.

( 3 + 5 i ) + ( 1 i )

By the Commutative and Associative Properties,

( 3 + 5 i ) + ( 1 i ) = ( 3 + ( 1 ) ) + ( 5 i + ( i ) )

Simplify.

= 2 + 4 i

The sum is 2 + 4 i .

Example 2:

Simplify.

( 3 2 i ) ( 5 4 i )

By the Commutative and Associative Properties,

( 3 2 i ) ( 5 4 i ) = ( 3 5 ) + [ 2 ( 4 ) ] i

Simplify.

= 2 + 2 i

The difference is 2 + 2 i .