Question

How do you simplify `2/(6-4i)`?

Answer 1

`(3/13)+(2/13)i`

Explanation:

Multiply numerator and denominator by the conjugate of the denominator.

nb: `(a+ib)(a-ib)-=a^2+b^2`

`2/(6-4i)=2/(6-4i)xx(6+4i)/(6+4i)`

`=(12+8i)/(6^2+4^2)`

`=(12+8i)/(52)=(12/52)+(8/52)i`

`=(3/13)+(2/13)i`