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AP EAMCET202418 May 2024Morning ShiftMathematicsComplex NumberActual

If Z =x+i y is a complex number, then the number of distinct solution of the equation z^3+ z =0 is

Options

  1. A1
  2. B3
  3. CInfinite
  4. D5

Correct answer

D. 5

Step-by-step solution

Given, z^3+ z =0 , where z=x+i y is a complex number aligned & z^3=- z |z^3 |=|- z | |z|^3=|z| & |z|^3-|z|=0 |z| (|z|^2-1 )=0 aligned aligned & |z|=0 or |z|^2=1 z z =1 z = 1 z & z=0 or z^3+ 1 z =0 z=0 or z^4+1=0 aligned So, total number of distinct solution of given equation is 5 .

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