1. Tardigrade
  2. Question
  3. Mathematics
  4. Let (-2 - (1/3) i )3 = (x+iy/27) (i = √-1) , where x and y are real numbers, then y - x equals :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 :

JEE MainJEE Main 2019Complex Numbers and Quadratic Equations

Solution:

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