Question

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

• A. -85
• B. 85
• C. -91
• D. 91

Answer 1

Answer: (D)

${\left(-2-\frac{i}{3}\right)}^3=-\frac{{\left(6+i\right)}^3}{27}$
$=\frac{-198-107i}{27}=\frac{x+iy}{27}$
Hence, $y-x=198-107=91$