Question

What is `(7+4i)/(6-8i)`?

Answer 1

`1/10+4/5i`

Explanation:

Multiply the expression by the complex conjugate.

`(7+4i)/(6-8i)((6+8i)/(6+8i))=(42+56i+24i+32i^2)/(36+48i-48i-64i^2)=(42+80i+32i^2)/(36-64i^2)`

Recall that since `i=sqrt(-1)`, we can say that `i^2=-1`.

`=(42+80i+32(-1))/(36-64(-1))=(10+80i)/100=1/10+4/5i`

Notice that the answer is written in the `a+bi` form of a complex number.