Solution
= Solution
Put $z=x+iy$. Comparing imaginary parts gives $-y=1$, so $y=-1$. Comparing real parts then gives $\sqrt{x^2+1}=x$. The left side is positive, so squaring is legitimate only with $x\geq0$, but even then it would give $x^2+1=x^2$. This contradiction proves \b[there is no solution]. Equivalently, with nonzero imaginary part the <complex modulus> is strictly greater than the real part.