Question:
Let $\left(-2-\frac{1}{3} i\right)^{3}=\frac{x+i y}{27}(i=\sqrt{-1})$, where $\mathrm{x}$ and $\mathrm{y}$ are real numbers then $y-x$ equals :
Correct Option: 1
Solution:
$-(6+i)^{3}=x+i y$
$\Rightarrow \quad-\left[216+i^{3}+18 i(6+i)\right]=x+i y$
$\Rightarrow \quad-[216-i+108 i-18]=x+i y$
$\Rightarrow \quad-216+i-108 i+18=x+i y$
$\Rightarrow \quad-198-107 i=x+i y$
$\Rightarrow \quad x=-198, y=-107$
$\Rightarrow \quad y-x=-107+198=91$
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