Question

Divide by rationalizing the denominator.

3+5i/10+3i


A. 25+47i/109
B. 60-18i/109
C. 100-30i/109
D. 45+41i/109

Answer 1

D

Explanation:

Multiply the numerator and denominator by the conjugate of the denominator.

Note that i² = - 1

The conjugate of 10 + 3i is 10 - 3i , then

`((3+5i)(10-3i))/((10+3i)(10-3i))` ← Expand numerator/denominator using FOIL

=
`(30-9i+50i-15i^2)/(100-30i+30i-9i^2)` ← simplify

=
`(30+41i+15)/(100+9)`

=
`(45+41i)/(109)` → D