Question

How do you simplify `(2-3i)/(1-2i)`?

Answer 1

`(8+i)/5`

Explanation:

Multiply both the numerator and the denominator by the conjugate of the denominator `1-2i`, which is `1+2i`: (since the conjugate of a complex number `a+bi` equals to `a-bi`)

`((2-3i)(1+2i))/((1-2i)(1+2i)=` `(2+4i-3i-6i^2)/(1^2 - (2i)^2)` = `(2+i+6)/(1-(-4))` `=(8+i)/5`