Question 1026767

I am having trouble with this complex number question, finding the reciprocal of this (3-i)/2
<pre>Now that's better. This is much, much clearer now!
{{{(3 - i)/2}}} 
{{{2/(3 - i)}}} ------- Reciprocal
{{{(2(3 + i))/((3 - i)(3 + i))}}} ---- Rationailizing denominator by multiplying fraction by the conjugate of the denominator
{{{2(3 + i)/(9 + 3i - 3i - i^2)}}}
{{{2(3 + i)/(9 - i^2)}}}
{{{2(3 + i)/(9 - - 1)}}} ------ Replacing {{{i^2}}} with - 1
{{{2(3 + i)/10}}}
{{{2(3 + i)/2(5)}}}
{{{cross(2)(3 + i)/cross(2)(5)}}} ------> {{{(3 + i)/5}}} ------> {{{highlight_green(matrix(1,3, 3/5, "+", (1/5)i))}}}