Evaluate the expression and write the result In the form a

Evaluate the expression and write the result In the form a + bl. (Simplify your answer completely.) 4/4 + i

Solution

4/(4+i)

rationalise denominator :multiply and divide by the conjugate of the denomiantor: 4-i

So, 4( 4-i)/( 16 +1)

= (16 -4i)/17

= 16/17 - (4/17)*i

=0.94 - 0.24*i

= a+bi