Hi,

I need to find the resulting vector of a resistor in parallel with a capacitance in parallel with an inductance.

The complex impedances are -J50 and J200. The value of the resistor is 100Ω

So i have \( \frac{1}{\frac{1}{100}+\frac{1}{-j50}+\frac{1}{j200}}\)

In the key to my textbook this should equate to 55.47\(\angle\) -56.31.

And i don't get that...

if I add the two complex impedances i have 100 + J150.

\(\frac{1}{1/100 +1/150} = 60 \angle 56.31\)

 

The text answer is correct - you need to re-check your method.

The components are in parallel - not in series. Adding the two complex terms as you have done would be OK if they in series.