Question 659314
<pre>
{{{bi/(c+di)}}}

Multiply by the unit fraction whose numerator and denominator 
are both the conjugate of the denominator of the given fraction.
 That is, we multiply by {{{(c-di)/(c-di)}}}

{{{bi/(c+di)}}}·{{{(c-di)/(c-di)}}} = {{{(bi(c-di))/((c+di)(c-di))}}} = {{{(bci-bdi^2)/(c^2-cdi+cdi-d^2i^2)}}} = {{{(bci-bdi^2)/(c^2-d^2i^2)}}} = 

{{{(bci-bd(-1))/(c^2-d^2(-1))}}} = {{{(bci+bd)/(c^2+d^2)}}} = {{{bci/(c^2+d^2)}}}+{{{bd/(c^2+d^2)}}} = {{{bd/(c^2+d^2)}}}+{{{bc/(c^2+d^2)}}}i

Edwin</pre>