# where x and y are real numbers then y-x equals :

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 :

1. (1) 91

2. (2) $-85$

3. (3) 85

4. (4) $-91$

Correct Option: 1

Solution:

$-(6+i)^{3}=x+i y$

$\Rightarrow \quad-\left[216+i^{3}+18 i(6+i)\right]=x+i y$

$\Rightarrow \quad-[216-i+108 i-18]=x+i y$

$\Rightarrow \quad-216+i-108 i+18=x+i y$

$\Rightarrow \quad-198-107 i=x+i y$

$\Rightarrow \quad x=-198, y=-107$

$\Rightarrow \quad y-x=-107+198=91$