Question

How do you divide `(2+3i)/(4-5i)`?

Answer 1

`-7/41 + 22/41 i`

Explanation:

To divide the fraction : multiply the numerator and denominator

by the 'complex conjugate' of 4 - 5i which is 4 + 5i . This

changes the denominator to a real number.

`((2 + 3i )(4 + 5i ))/((4 - 5i )(4 + 5i )`

( distribute brackets using FOIL method )

`( 8 + 10i + 12i + 15i^2 )/(16 + 20i -20i - 25i^2)`

(Note : `i^2 = - 1 )`

`= (8 + 22i -15 )/(16 + 25 ) = (- 7 + 22i )/( 16 + 25 ) = -7/41 + 22/41 i`