Let the complex Z satisfy ZZ - + (2-I) Z + (2 + I) Z - + 4 = 0, and prove the distance from the point corresponding to Z on the complex plane to the point corresponding to complex - 2-I on the complex plane constant Z - is the conjugate complex number of Z, which is convenient to type

Let the complex Z satisfy ZZ - + (2-I) Z + (2 + I) Z - + 4 = 0, and prove the distance from the point corresponding to Z on the complex plane to the point corresponding to complex - 2-I on the complex plane constant Z - is the conjugate complex number of Z, which is convenient to type

Let z = x + Yi
zz-+(2-i)z+(2+i）z- +4=0
x^2+y^2+(2-i)(x+yi)+(2+i)(x-yi)+4=0
x^2+y^2+2x+2yi-xi+y+2x-2yi+xi+y+4=0
x^2+y^2+4x+2y+4=0
(x + 2) ^ 2 + (y + 1) ^ 2 = 1
|z-(-2-i)|=1
So the original formula holds

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