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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

Answers (1)

best_answer

 

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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