QJEEM19Maff54: JEE Main 2019 Mathematics - Class 11 JEEM19Maff54 Solution: Let ( − 2 − 1 3 i ) 3 = x + i y 27 ( i = − 1 ) , where x and y…

Question

Verified Solution • 2025–26 Session moderate

Let

{(- 2 - \frac{1}{3} i)}^{3} = \frac{x + i y}{27} (i = \sqrt{- 1}),

where x and y are real numbers, then y

-

x equals :

Accepted Answer

{(- 2 - \frac{i}{3})}^{3} = - \frac{{(6 + i)}^{3}}{27}

= \frac{- 198 - 107 i}{27} = \frac{x + i y}{27}

Hence,

y - x = 198 - 107 = 91

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