SOLUTION: This is from a worksheet. simplify 2+i/1-3i please help Thank you

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Question 162014: This is from a worksheet.
simplify
2+i/1-3i
please help
Thank you
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%282%2Bi%29%2F%281-3i%29 Start with the given expression


%28%282%2Bi%29%2F%281-3i%29%29%28%281%2B3i%29%2F%281%2B3i%29%29 Multiply both numerator and denominator by 1%2B3i. Note: this is the complex conjugate of the denominator


%28%282%2Bi%29%281%2B3i%29%29%2F%28%281-3i%29%281%2B3i%29%29 Combine the fractions


%282%2B6i%2Bi%2B3i%5E2%29%2F%281%2B3i-3i-9i%5E2%29 FOIL


%282%2B7i%2B3i%5E2%29%2F%281-9i%5E2%29 Combine like terms.


%282%2B7i%2B3%28-1%29%29%2F%281-9%28-1%29%29 Replace i%5E2 with -1


%282%2B7i-3%29%2F%281%2B9%29 Multiply


%28-1%2B7i%29%2F%2810%29 Combine like terms.


-1%2F10%2B%287%2F10%29i Break up the fraction


So the answer is -1%2F10%2B%287%2F10%29i. Notice how it is in standard form a%2Bbi where a=-1%2F10 and b=7%2F10