# complex numbers ?

A resistor is connected in series with a capacitor; both components are connected in parallel with an inductor across a supply voltage of 10v at 1,2 k Hz

a) Calculate the capacitive and inductive reactance values; show all your method

b) Represent the circuit as a single impedance value using the formula below, express your solution in Cartesian form and Polar form; show all your method to obtain the solution

Ztotal=(z1*z2)/(z1+z2)

a) Express Z Total in polar form; show all stages of your method

### 6 Answers

- qrkLv 74 weeks agoBest answer
Simply solve this as you would if you had a bunch of resistors except use imaginary numbers for the capacitor and inductor reactances. You need to know how to arithmetically manipulate complex numbers which should have been taught in high school algebra. I would put the answer in a + jb form (j is the imaginary operator). From this you can easily convert to polar.

To start you out,

Xc = 1/jwC

XL = jwL

where w is the angular frequency = 2*pi*f

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could you kindly help me with the next step please? Thank you