Let (-2-13 i)^3=x+iy27 (i=-1), where x,y are real numbers.

Question

Let $\left(-2-\dfrac13 i\right)^3=\dfrac{x+iy}{27}$ ($i=\sqrt{-1}$), where $x,y$ are real numbers. Then $y-x$ equals:

Accepted Answer

$27\left(-2-\dfrac13i\right)^3=(-6-i)^3=-(6+i)^3=-198-107i$ (expanding), so $x=-198,\ y=-107$.

$y-x=-107-(-198)=91.$

Solutions · 1