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Express $\;(- \sqrt{3} + \sqrt{-2})(2 \sqrt{3} - i)\;$ in the form $\;a+ib$

$(a)\;(-3+\sqrt{2})+\sqrt{3}(1+2\sqrt{2}) i \qquad(b)\;(-6+\sqrt{3})+\sqrt{3}(1+\sqrt{2}) i \qquad(c)\;(-1+\sqrt{2})+\sqrt{2}(1+2\sqrt{2}) i \qquad(d)\;(-6+\sqrt{2})+\sqrt{3}(1+2\sqrt{2}) i $

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Answer : $\;(-6+\sqrt{2})+\sqrt{3}(1+2\sqrt{2}) i$
Explanation :
$\;(- \sqrt{3} + \sqrt{-2})(2 \sqrt{3} - i)\; = ( -\sqrt{3} + \sqrt{2} i)(2 \sqrt{3} -i)$
$= - 6 + i \sqrt{3} + 2 \sqrt{6} i - \sqrt{2} i^{2}$
$ = (-6+\sqrt{2})+\sqrt{3}(1+2\sqrt{2}) i \;.$
answered Apr 16, 2014 by yamini.v
 
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