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Question

Mathematics Question on Complex Numbers and Quadratic Equations

−3−6\sqrt{-3}\sqrt{-6} is equal to

A

323\sqrt{2}

B

−32-3\sqrt{2}

C

32 i3\sqrt{2}\,i

D

−32 i-3\sqrt{2}\,i

Answer

−32-3\sqrt{2}

Explanation

Solution

−3=i3\sqrt{-3}=i\sqrt{3}, −6=i6\sqrt{-6}=i\sqrt{6} So, (−3)(−6)\sqrt{\left(-3\right)}\sqrt{\left(-6\right)} =i2 32=i^{2} \,3\sqrt{2} =−32=-3\sqrt{2}