Let the function

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

  1. –85 

  2. 85

  3. –91

  4. 91 


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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