Question

How do you divide `(-5-3i) -: (7-10i)`?

Answer 1

`(-5-3i)/(7-10i) = -5/149-71/149i`

Explanation:

We can multiply both numerator and denominator by the complex conjugate `7+10i` as follows:

`(-5-3i)/(7-10i) = ((-5-3i)(7+10i))/((7-10i)(7+10i))`

`color(white)((-5-3i)/(7-10i)) = ((-5)(7)+(-5)(10i)+(-3i)(7)+(-3i)(10i))/((7)^2-(10i)^2)`

`color(white)((-5-3i)/(7-10i)) = (-35-50i-21i+30)/(49+100)`

`color(white)((-5-3i)/(7-10i)) = (-5-71i)/149`

`color(white)((-5-3i)/(7-10i)) = -5/149-71/149i`