Find the value of the following expression in terms of

allhvasstH 2021-08-16 Answered
Find the value of the following expression in terms of a+bi:
\(\displaystyle\frac{\sqrt{{-{6}}}}{{\sqrt{{-{3}}}\sqrt{{-{4}}}}}\)

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Expert Answer

coffentw
Answered 2021-08-17 Author has 5063 answers
\(\displaystyle\frac{{{i}\sqrt{{6}}}}{{{i}\sqrt{{3}}\times{i}\sqrt{{4}}}}=\frac{{-{i}\sqrt{{6}}}}{{{2}\sqrt{{3}}}}=\frac{{-{i}\sqrt{{\frac{{6}}{{3}}}}}}{{2}}=\frac{{-{i}\sqrt{{2}}}}{{2}}\)
So,
\(\displaystyle\frac{\sqrt{{-{6}}}}{{\sqrt{{-{3}}}\sqrt{{-{4}}}}}=\frac{{-{i}\sqrt{{\frac{{6}}{{3}}}}}}{{2}}=\frac{{-{i}\sqrt{{2}}}}{{2}}\)
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