Question:
Let $\left(-2-\frac{1}{3} \mathrm{i}\right)^{3}=\frac{\mathrm{x}+\mathrm{iy}}{27}(\mathrm{i}=\sqrt{-1})$, where $\mathrm{x}$
and $\mathrm{y}$ are real numbers, then $\mathrm{y}-\mathrm{x}$ equals
Correct Option: , 4
Solution:
$\left(-2-\frac{1}{3}\right)^{3}=-\frac{(6+i)^{3}}{27}$
$=\frac{-198-107 \mathrm{i}}{27}=\frac{x+i y}{27}$
Hence, $\mathrm{y}-\mathrm{x}=198-107=91$
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