3/(3 - 12i)
To simplify this, multiply both sides by (3 + 12i)
(3 - 12i)(3 + 12i)
Distributive property.
3(3 + 12i) - 12i(3 + 12i)
9 + 36i - 36i - 144i^2
Simplify.
9 - 144i^2
i^2 can be interpreted as -1.
9 + 144
Combine like terms.
153 is the simplified version of the bottom half of the expression.
Now for the top half.
3(3 + 12i)
Distributive property.
9 + 36i
We can simplify this further by factoring.
3(3 + 12i)/153
1 + 4i/17
1/17 + 4i/17 is the simplified version of the expression. (This is your answer.)
Let me know if you have any other questions.