SOLUTION: Rationalize the denominator: {{{5/(1-sqrt(3))}}} Divide {{{2/(3+2i)}}}

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator: {{{5/(1-sqrt(3))}}} Divide {{{2/(3+2i)}}}      Log On


   



Question 145391: Rationalize the denominator:
5%2F%281-sqrt%283%29%29
Divide
2%2F%283%2B2i%29

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator:

5%2F%281-sqrt%283%29%29
Divide
2%2F%283%2B2i%29
 
5%2F%281-sqrt%283%29%29

Form the conjugate of the denominator, which is 1%2Bsqrt%283%29,
then multiply by +%28%281%2Bsqrt%283%29%29%29%2F%28%281%2Bsqrt%283%29%29%29+

5%2F%281-sqrt%283%29%29*+%28%281%2Bsqrt%283%29%29%29%2F%28%281%2Bsqrt%283%29%29%29+

5%2F%28%281-sqrt%283%29%29%29*+%28%281%2Bsqrt%283%29%29%29%2F%28%281%2Bsqrt%283%29%29+%29

5%281%2Bsqrt%283%29%29%2F%28%281-sqrt%283%29%29%281%2Bsqrt%283%29%29%29

5%281%2Bsqrt%283%29%29%2F%28%281%2Bsqrt%283%29-sqrt%283%29-%28sqrt%283%29%29%5E2%29%29

5%281%2Bsqrt%283%29%29%2F%28%281%2B%28sqrt%283%29%29%5E2%29%29
5%281%2Bsqrt%283%29%29%2F%281-3%29
5%281%2Bsqrt%283%29%29%2F%28-2%29
%28-5%2F2%29%281%2Bsqrt%283%29%29
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3 and 2 over 3 + 2i
 
2%2F%283%2B2i%29

Form the conjugate of the denominator, which is 3-2i,
then multiply by +%28%283-2i%29%29%2F%28%283-2i%29%29+

2%2F%283%2B2i%29*+%28%283-2i%29%29%2F%28%283-2i%29%29+

2%2F%28%283%2B2i%29%29+%28%283-2i%29%29%2F%28%283-2i%29+%29

2%283-2i%29%2F%28%283%2B2i%29%283-2i%29%29

2%283-2i%29%2F%28%289-6i%2B6i-%282i%29%5E2%29%29
2%283-2i%29%2F%28%289-cross%286i%2B6i%29-%282i%29%5E2%29%29
2%283-2i%29%2F%28%289-%282i%29%5E2%29%29
2%283-2i%29%2F%289-4i%5E2%29
2%283-2i%29%2F%289-4%28-1%29%29
2%283-2i%29%2F%289%2B4%29
2%283-2i%29%2F13
%282%2F13%29%283-2i%29
That would do for an answer. But sometimes
you are asked to leave a complex number in
the form a%2Bbi
So you would distribute that out:
%282%2F13%293-%282%2F13%292i
6%2F13-%284%2F13%29i
Edwin