Question

The a+ib form of (5-3i)/(6+i) is?

Answer 1

Step-by-step explanation:

we have to mutilpy both numerator and denominator, with (6-i) to rationalize.

so {(5-3i)×(6-i)}/{ (6+i)×(6-i)} = (30 - 18 i - 5 i + 3 i^2 )/ (6 - i^2)

= 30 - 23 i +3 (-1) }/ {6 - i ^2 }

=( 30 - 23 i -3 )/ 6 - ( -1 ) since i^2 = -1 .

=( 27 - 23 i ) / 7 .

So in a+ib form we have (27/7) +i(-23/7 ) . where a= 27/7 and b= -23/7