Question 834066
<pre>
{{{(5+8i)/(3+5i)}}}

The conjugate of the denominator is 3-5i.  Multiply
the expression by {{{(3-5i)/(3-5i)}}} which equals 1:

{{{(5+8i)/(3+5i)}}}{{{""*""}}}{{{(3-5i)/(3-5i)}}}

{{{((5+8i)(3-5i))/((3+5i)(3-5i))}}}

FOIL out the top and bottom:

{{{(15-25i+24i-40i^2)/(9-15i+15i-25i^2)}}}

{{{(15-i-40i^2)/(9-25i^2)}}}

Now replace {{{i^2}}} by {{{-1}}}:

{{{(15-i-40(-1))/(9-25(-1))}}}

{{{(15-i+40)/(9+25)}}}

{{{(55-i)/34}}}

{{{55/34}}}{{{""-""}}}{{{expr(1/34)i}}}

Edwin</pre>