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Question

The real values of x and y for which (x13+i+y13i)=i is
  1. x=4 and y=6
  2. x=6 and y=3
  3. x=2 and y=8
  4. x=8 and y=6


Solution

The correct option is A x=4 and y=6
We have
(x13+i+y13i)=i
(x1)(3i)+(y1)(3+i)32i2=i
3(x+y2)i(xy)10=i
3(x+y2)=0 and (yx)=10
[equating real parts and the imaginary parts seperately]
x+y2=0 and yx=10
x=4 and y=6   

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