To simplify a number with a complex denominator, we need to utilize the complex conjugate. For any complex number a+bi, its complex conjugate, bar (a+bi), is the complex number a-bi. The conjugate is remarkably handy in turning complex denominators into real ones, which, in this case, will allow us to break apart our fraction into a real and imaginary part of the form a+bi.
When we multiply a+bi by bar (a+bi), we can remember the fact that the particular case of the binomials (a+b)(a-b) has the product a^2-b^2. Since i has the special property that i^2=-1, (a+bi)(a-bi) actually ends up giving us a^2+b^2; this is especially convenient, as the imaginary part is completely eliminated in the product.
Turning out attention back to the problem, we'd like to turn the denominator into a real number, but we can't change the value of our number as a whole, so we'll have to multiply it by some form of 1. To get our denominator 2-3i into the right form, we'll choose the fraction bar(2-3i)/bar(2-3i), or (2+3i)/(2+3i).
Multiplying that out, we get:
(7i)/(2-3i)*(2+3i)/(2+3i)=(7i(2+3i))/((2-3i)(2+3i))
The denominator, as mentioned before, becomes 2^2+3^2=13, and distributing the 7i to the 2 and the 3i in the numerator gets us 14i-21. Altogether, we have
(14i-21)/13
which we can break apart into
(14i)/13-21/13
and rearrange into the form a+bi:
-21/13+14/13i