How do you find the quotient of #(\sqrt{3}-i) -: (2- 2\sqrt{3}i)#?

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Answer 1 · 2014-11-06T16:23:59

#(sqrt{3}-i) divide (2-i2sqrt{3})#

by rewriting in fraction form,

#={sqrt{3}-i}/{2-2sqrt{3}i}#

by factoring #2# out of the denominator,

#={sqrt{3}-i}/{2(1-sqrt{3}i)}#

by multiplying the numerator and the denominator by #(1+sqrt{3}i)#,

#={sqrt{3}+3i-i+sqrt{3}}/{2[1-(sqrt{3}i)^2]}#

by simplifying a bit further,

#={2(sqrt{3}+i)}/{2(1+3)}#

by cancelling out #2#,

#={sqrt{3}+i}/4#

I hope that this was helpful.