Complex impedance of parallel RC circuit

[eng_stud]

In my book (Storey), there's an exercise with a parallel RC circuit, where R = 80 Ohm and C = 30 uF. The answer for the complex impedance is supposed to be 40-j40, however I can't seem to get there! I've showed my working under. Am I doing something wrong, or is the book's answer wrong? (freq =200 Hz)

$$\frac{Z_R Z_C}{Z_R +Z_C} = \frac{-RjX_C}{R-jX_C} \frac{R+jX_C}{R+jX_C}$$

$$\frac{RX_C^2 -R^2 j X_C}{R^2 + X_C^2} = \frac{R(1/\omega C)^2 - jR^2 (1/\omega C)}{R^2 + (1/\omega C)^2}$$

$$= \frac{80*(\frac{1}{2 \pi *200 * 30 *10^{-6}})^2 - j80^2 * (\frac{1}{2\pi * 200* 30 *20^{-6}} ) }{80^2 + (\frac{1}{2\pi * 200 * 30*10^{-6}})^2}$$

$$= \frac{56289.5 - j169765.3}{7103.6} \approx = 8 - j23$$

Am I just too tired when doing these calculations?;-)

Thanks!

 

[vela]

Your work is fine.

 

[eng_stud]

Thanks!