Question

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

Answer 1

`-10/41+8/41i`

Explanation:

Multiply by the complex conjugate.

`frac(2i)(4-5i)(frac(4+5i)(4+5i))=frac(8i+10i^2)(16+20i-20i-25i^2)=frac(8i+10i^2)(16-25i^2)`

Recall that `i=sqrt(-1)`, so `i^2=-1`.

`frac(8i+10(-1))(16-25(-1))=frac(8i-10)(16+25)=(-10+8i)/41`

In the form of a complex number, this would be written as:

`-10/41+8/41i`