Let -2-13i3-x-iy27 i-1- where x and y are real numbers- then y-x equals-

The correct option is D 91 Calculating: ( 2 i3)^3=( 6 i)^327 = 198 107i27=x+iy27 #160;Hence, y x=198 107=91 ...

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Standard XII

Mathematics

Algebra of Complex Numbers

Let -2-13i3...

Question

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:

- 85

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85

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- 91

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91

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Solution

The correct option is D $91$
Calculating: ${(- 2 - \frac{i}{3})}^{3} = \frac{(- 6 - i)^{3}}{27}$
$= \frac{- 198 - 107 i}{27} = \frac{x + i y}{27}$
Hence, $y - x = 198 - 107 = 91$

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Let (−2−13i)3=x+iy27 (i=√−1), where x and y are real numbers, then y−x equals:

The correct option is D 91Calculating: (−2−i3)3=(−6−i)327=−198−107i27=x+iy27 Hence, y−x=198−107=91

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:

The correct option is D $91$
Calculating: ${(- 2 - \frac{i}{3})}^{3} = \frac{(- 6 - i)^{3}}{27}$
$= \frac{- 198 - 107 i}{27} = \frac{x + i y}{27}$
Hence, $y - x = 198 - 107 = 91$