Question

Simplify.

4-3i/6-4i


A. 18-i/26
B. 15-3i/26
C. -4+3i
D. 3+2i/13

Answer 1

A

Explanation:

To simplify the expression multiply the numerator and denominator by the conjugate of the denominator.

Note that i² = - 1

The conjugate of 6 - 4i is 6 + 4i , then

=
`((4-3i)(6+4i))/((6-4i)(6+4i))` ← expand numerator./ denominator using FOIL

=
`(24+16i-18i-12i^2)/(36+24i-24i-16i^2)`

=
`(24-2i+12)/(36+16)`

=
`(36-2i)/(52)`

=
`(2(18-i))/(52)`

=
`(18-i)/(26)` → A