Let z be a complex number of constant modulus such that z*z is purely imaginary then the number of possible values of z is?

let z=x+iy, x^2 + y^2 is constant. z*z=x^2 - y^2 +i2xy is purely imaginary implies that x=±y,x^2+y^2=2x^2=k,k>0, so there are 2 possible values of z

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