Solving complex equation: Z │ Z │ + AZ + I = 0 (a > = 0)

z=x+iy
(x+iy)(x^2+y^2)^(1/2)+a(x+iy)+i=0
There is x [√ (x ^ 2 + y ^ 2) + a] = 0
y√(x^2+y^2)+ay+1=0②
Get x = 0 or x = y = a = 0 from ① (not satisfied with ②, rounding off)
So y │ y │ + ay + 1 = 0
When y > = 0, there is no solution
When y

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