Question

Rationalize and Simplify
5i - 2i
-----
1 - 2i

Answer 1

multiply by 1+2i to realize the denominator
you then get (3i - 6)/5

Answer 2

wait what??can you explain?

Answer 3

Your numerator = 5i -2i = 3i
Now, your denominator has to be free of all i's. How do we cancel out the i in the denominator? We multiply 1-2i by 1+2i (but to be valid, we need to multiply the top by 1+2i as well)

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