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AP EAMCET201823 Apr 2018Morning ShiftMathematicsComplex NumberActual

If u+i v= 3 i x+i y+2 , then y=

Options

  1. A9 u u^2+v^2
  2. B3 u u^2+v^2
  3. C6 u u^2+v^2
  4. D12 u u^2+v^2

Correct answer

B. 3 u u^2+v^2

Step-by-step solution

aligned & We have, u+i v= 3 i x+i y+2 & x+i y+2= 3 i u+i v & (x+2)+i y= 3 i u+i v + u-i v u-i v = 3 u i-3 v (i^2 ) u^2-(i v)^2 & (x+2)+i y= 3 u i+3 v u^2+v^2 & (x+2)+i y= 3 v u^2+v^2 + 3 u u^2+v^2 i aligned by comparing Imaginary parts y= 3 u u^2+v^2

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