Question

Let ${(-2-\frac{1}{3}i)}^3=\frac{x+iy}{27}(i=\sqrt{-1})$, where $x$ and $y$ are real numbers, then $y-x$ equals :

• A. $91$
• B. $85$
• C. $-91$
• D. $-85$

Answer 1

The correct option is A $91$

${(-2-\frac{1}{3}i)}^3=\frac{x+iy}{27}\Rightarrow (6+i{)}^3=-x-iy$
$\Rightarrow 216+i^3+18i^2+108i=-x-iy$
$\Rightarrow 198+107i=-x-iy$
$\Rightarrow x=-198$ and $y=-107$
$\Rightarrow y-x=91$