Question

Which is the imaginary part in the complex number $3+\sqrt{-216}i?$

• A. 10
• B. $6\sqrt{6}$
• C. $108\sqrt{2}$
• D. None of the above

Answer 1

The correct option is B $6\sqrt{6}$

Given, $3+\sqrt{-216}i$

$\sqrt{-216}=\sqrt{216\times -1}=\sqrt{6\times 6\times 6\times -1}=\sqrt{6^2\times 6}\times \sqrt{-1}=6\sqrt{6}i$

Hence, $3+\sqrt{-216}$ = 3 + $6\sqrt{6}i$
Comparing $3+6\sqrt{6}i$ with the standard form of a complex number, $a+ib$, we get the imaginary part as $6\sqrt{6.}$