I'm reading control systems engineering 7th by nise. The author discusses a second-order system with two poles and no zeros. In the s-domain, the system is represented as
$$ \frac{b}{s^2 + as + b} $$
where $a$ and $b$ are constant numbers and $s$ a complex variable. If we define $w_n = \sqrt{b}$ and $\zeta = \frac{a}{2 w_n}$ to be the natural frequency and the damping ratio, respectively, the the poles of the system in case underdamped system is
$$ s_{1,2} = - \zeta w_n \pm (w_n \sqrt{\zeta^2-1} ) $$
which is the equation numbered in the book as (4.24). So far so good. The plot of these poles in the complex plane is (i.e. Figure 4.11 in the book)
Why in the plot, the imaginary value differs from the equation while the real value is the same?