Missing steps to simplify this complex impedance
It's clearly a mistake by your textbook, as mentioned in the comments.

$$\frac{1000\cdot j1591.6}{1000+j1591.6}=\frac{1000\cdot j1591.6}{1000+j1591.6}\cdot\frac{1000-j1591.6}{1000-j1591.6}=\frac{10^6\cdot (j1591.6-j^2 2533.19056)}{10^6\cdot(1+j1.5916-j1.5916-j^2 2.53319056)}|_{j^2=(-1)}=\frac{j1591.6+2533.19056}{3.53319056}=\frac{2533.19056}{3.53319056}+j\frac{1591.6}{3.53319056}\approx716.97+j450.47$$

So, multyplying by the complex conjugate of the denominator works to get the result provided by both @Null and @jippie.