Question 582408
In order for the fraction to remain the
same, the top and bottom must be multiplied
by the same thing. 
{{{ (( 10 + 5i ) / ( 10 - 5i )) * (( 10 + 5I ) / ( 10 + 5i ))
{{{ ( 10 + 5i )^2 / ( 100 - ( 5i)^2 ) }}}
{{{ ( 10 + 5i )^2 / ( 100 -(-25) ) }}}
{{{ ( 10 + 5i )^2 /  125 }}}
{{{ ( 100 + 10i + 25*(-1) ) / 125 }}}
{{{ ( 75 + 10i ) / 125 }}}
{{{ 3/5 + (2/25)*i }}}
Unless I messed it up, this is it