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AP EAMCET202421 May 2024Evening ShiftMathematicsComplex NumberActual

The square root of 7+24 i

Options

  1. A4-3 i
  2. B3+4 i
  3. C3-4 i
  4. D4+3 i

Correct answer

D. 4+3 i

Step-by-step solution

Let 7+24 i =x+i y 7+24 i= (x^2-y^2 )+2 x y i Equating real and imaginary parts aligned & x^2-y^2=7 and 2 x y=24 y= 12 x & x^2- ( 12 x )^2=7 x^4-7 x^2-144=0 & x^2=16,-9 x= 4, y= 3 aligned So, (x+i y)= (4+3 i) .

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