Question 151802
<pre><font size = 4 color = "indigo"><b>

{{{(7-i)/(-1+3i)}}}

Form the conjugate of the denominator by
1. Writing the first term.   {{{-1}}}
2. Beside the first term write the second
term with the sign before it changed. 
                             {{{-1-3i}}}

Put parentheses around top and bottom of original:

{{{((7-i))/((-1+3i))}}}

Multiply top and bottom by the conjugate of the
denominator placed in parentheses:

{{{((7-i)(-1-3i))/((-1+3i)(-1-3i))}}}  

Now use FOIL to multiply out the top and bottom:

{{{(-7-21i+i+3i^2)/(1+3i-3i-9i^2))}}}

Combine like terms:

{{{(-7-20i+3i^2)/(1-9i^2))}}}

Replace both {{{i^2}}}'s by {{{-1}}}:

{{{(-7-20i+3(-1))/(1-9(-1)))}}}

Simplify:

{{{(-7-20i-3)/(1+9)}}}

Simplify further:

{{{(-10-20i)/10}}}

Make two fractions:

{{{-10/10-20i/10}}}

Simplify:

{{{-1-2i}}}

Edwin</pre>