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# Solve this problem - Let, where x ad y are real numbers, then equals: - Complex numbers and quadratic equations - JEE Main

Let $(-2-\frac{1}{3}i\: )^{3} = \frac{x+iy}{27}\: \: (i=\sqrt{-1})$ ,  where x ad y are real numbers,

then $y-x$ equals:

• Option 1)

91

• Option 2)

-91

• Option 3)

-85

• Option 4)

85

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Equality in Complex Numbers -

z=x+iy & w=a+ib are equal iff x=a & y=b

- wherein

Two complex numbers are equal iff real parts as well as imaginary parts are equal.

$\left ( -2-\frac{1}{3} \right )^{3}=-\frac{1}{27}\left ( 6+i \right )^{3}$

$=-\frac{1}{27}\left ( 216+108i+18i^{2}+i^{3} \right )$

$=-\frac{1}{27}\left ( 198+107i \right )$

$x=-198\; \; \; \; \; \; \; \; \; y=-107$

$\Rightarrow y-x=91$

Option 1)

91

Option 2)

-91

Option 3)

-85

Option 4)

85

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