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AP EAMCET20226 Jul 2022Morning ShiftMathematicsComplex NumberActual

The number of complex numbers z satisfying z =i z^2 is

Options

  1. A3
  2. B4
  3. C2
  4. D5

Correct answer

B. 4

Step-by-step solution

Given equation is Z = iz ^2...(i) Let Z = x + iy Z = x - iy Now, from equation (i) aligned & x-i y=(x+i y)^2 & x-i y=i (x^2-y^2+2 i x y ) & x-i y=i x^2-i y^2-2 x y & 2+2 x y=0 and y=y^2-x^2 aligned On solving get (0,0)(0,1) ( - 3 2 , -1 2 ) ( 3 2 , -1 2 ) are four solutions

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