It is known that the complex number Z satisfies | Z | = 2, and the imaginary part of Z2 is 2. (I) find Z; (II) let the corresponding points of Z, Z2, z-z2 in the complex plane be a, B, C respectively, and find the area of △ ABC

It is known that the complex number Z satisfies | Z | = 2, and the imaginary part of Z2 is 2. (I) find Z; (II) let the corresponding points of Z, Z2, z-z2 in the complex plane be a, B, C respectively, and find the area of △ ABC

(1) Let z = x + Yi (x, y ∈ R) let z = x + X + Yi (x, y, y ∈ R) from the title to get Z2 = (X-Y) 2 = (X-Y) 2 = (X-Y) 2 = (X-Y) 2 (2) (1) 2x2 = (X-Y) 2 = 2 = (X-Y) 2 = 2 (X-Y) 2 = 2 (X-Y) 2 = 2 (X-Y) 2 = 2 = x2-y-2 + 2 = x2-2 + 2xyi x \\x {(2) for (x = 1 + I) when z = 1 + I, Z2 = 2I, z-z2 = 2I, z-zz-zz2 = 2 = 2 = 2 = 2-z2 = 2 = 1-2 = 1-I, z-zzzz2 = 2 = 1-2 = 1-I, so a (1-1-i 2 = 1 when z = - 1-I, Z2 = 2I, z-z2 = - 1-3i, a (- 1, -1），B（0，2），C（-1，3）S△ABC=12×1×4=2．