The existence of complex Z satisfies the following conditions: (1) the corresponding point of complex Z in the complex plane is in the second quadrant; (2) the value range of a is determined by multiplying Z by the conjugate complex Z + 2iz = 8 + AI (a ∈ R)

Let z = x + Yi
Then Z * Z (total) = (x + Yi) (x-yi) = x ^ 2-y ^ 2 * I ^ 2 = x ^ 2 + y ^ 2
(x^2+y^2)+2i(x+yi)=8+ai
According to the equality condition of complex number: (real part = real part, imaginary part = imaginary part)
(x^2+y^2)-2y=8
2x=a
.
Substituting x = A / 2 into the equation of circle, we get: (A / 2) ^ 2 = - y ^ 2 + 2y-1 + 9 = - (Y-1) ^ 2 + 9
(a/2)^2≤9
-3≤a/2≤3
-6≤a≤6

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