Given Z - | Z | = - 1 + I, find the complex Z

Given Z - | Z | = - 1 + I, find the complex Z

Let z = a + bi
arcsinx-x
a+bi-√(a^2+b^2)=-1+i
Compare the two sides
a-√(a^2+b^2)=-1
b=1
arcsinx-x
a-√(a^2+1)=-1
-√(a^2+1)=-1-a
Square gain
a^2+1=a^2+2a+1
a=0
So z = I