Let -2-13i 3-x-iy27 i-1- where x and y are real numbers- then y-x equals-

Given: ( 2 13i )^3=x+iy27 ⇒ (6+i)^3= x iy ⇒ 216 +i^3 + 18i^2+ 108i = x iy ⇒ 198 +107i = x iy ⇒ x = 198 and y= 107 ⇒ y x=91 ...

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Standard XIII

Mathematics

Algebra of Complex Numbers

Let -2-13i 3=...

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:

91

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85

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- 91

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Solution

The correct option is A $91$
${(- 2 - \frac{1}{3} i)}^{3} = \frac{x + i y}{27} \Rightarrow (6 + i)^{3} = - x - i y \Rightarrow 216 + i^{3} + 18 i^{2} + 108 i = - x - i y \Rightarrow 198 + 107 i = - x - i y \Rightarrow x = - 198 and y = - 107 \Rightarrow y - x = 91$

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Algebra of Complex Numbers

Standard XIII Mathematics

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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 A 91(−2−13i)3=x+iy27⇒(6+i)3=−x−iy⇒216+i3+18i2+108i=−x−iy⇒198+107i=−x−iy⇒x=−198 and y=−107⇒y−x=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 A $91$
${(- 2 - \frac{1}{3} i)}^{3} = \frac{x + i y}{27} \Rightarrow (6 + i)^{3} = - x - i y \Rightarrow 216 + i^{3} + 18 i^{2} + 108 i = - x - i y \Rightarrow 198 + 107 i = - x - i y \Rightarrow x = - 198 and y = - 107 \Rightarrow y - x = 91$