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

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Question 151802: %287-i%29%2F%28-1%2B3i%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


%287-i%29%2F%28-1%2B3i%29

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:

%28%287-i%29%29%2F%28%28-1%2B3i%29%29

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

%28%287-i%29%28-1-3i%29%29%2F%28%28-1%2B3i%29%28-1-3i%29%29  

Now use FOIL to multiply out the top and bottom:

%28-7-21i%2Bi%2B3i%5E2%29%2F%281%2B3i-3i-9i%5E2%29%29

Combine like terms:

%28-7-20i%2B3i%5E2%29%2F%281-9i%5E2%29%29

Replace both i%5E2's by -1:

%28-7-20i%2B3%28-1%29%29%2F%281-9%28-1%29%29%29

Simplify:

%28-7-20i-3%29%2F%281%2B9%29

Simplify further:

%28-10-20i%29%2F10

Make two fractions:

-10%2F10-20i%2F10

Simplify:

-1-2i

Edwin