Question

Express the following expression in the form of a + ib .

Answer 1

The given expression is ( 3+i 5 )( 3−i 5 ) ( 3 + 2 i )−( 3 −i 2 ) .

Simplify the given expression by using the formula ( a+b )( a−b )= a 2 − b 2 .

( 3+i 5 )( 3−i 5 ) ( 3 + 2 i )−( 3 −i 2 ) = ( 3 ) 2 − ( i 5 ) 2 3 + 2 i− 3 + 2 i = 9−5 ( i ) 2 2 2 i = 9−5( −1 ) 2 2 i = 9+5 2 2 i

Further simplify the above expression.

( 3+i 5 )( 3−i 5 ) ( 3 + 2 i )−( 3 −i 2 ) = 9+5 2 2 i × i i = 14i 2 2 ( −1 ) = −7i 2 × 2 2 = −7 2 i 2

Compare the above expression by a+ib.

Thus, the value of expression in the form of a+ib is 0+i −7 2 2 = −7 2 i 2 .