Answer:
see explanation
Step-by-step explanation:
We require to rationalise the denominator by multiplying the numerator and denominator by the complex conjugate of the denominator.
The conjugate of 5 + 3i is 5 - 3i
noting that i² = - 1, hence
[tex]\frac{(9-6i)(5-3i)}{(5+3i)(5-3i)}[/tex] ← expand factors
= [tex]\frac{45-57i+18i^2}{25-9i^2}[/tex]
= [tex]\frac{45-57i-18}{25+9}[/tex]
= [tex]\frac{27-57i}{34}[/tex]
= [tex]\frac{27}{34}[/tex] - [tex]\frac{57}{34}[/tex] i ← quotient
