Question

What does `(2i)/(4-5i)` equal?

Answer 1

`(2i)/(4-5i) = -10/41+8/41 i`

Explanation:

Multiply numerator and denominator by the conjugate `(4+5i)` of the denominator and simplify...

`(2i)/(4-5i) = (2i(4+5i))/((4-5i)(4+5i)) = (-10+8i)/(4^2+5^2) = (-10+8i)/(16+25) = (-10+8i)/41 = -10/41+8/41 i`