Question

Find the quotient. 9-6i/5+3i

Answer 1

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

$\frac{(9-6i)(5-3i)}{(5+3i)(5-3i)}$ ← expand factors

= $\frac{45-57i+18i^2}{25-9i^2}$

= $\frac{45-57i-18}{25+9}$

= $\frac{27-57i}{34}$

= $\frac{27}{34}$ - $\frac{57}{34}$ i ← quotient