Phase difference RLC circuit

[Tesla In Person]

For a parallel RLC circuit, I have found the complex impedance to be 1/ (1/R -j(1/wL +wC)) . I need to find the phase difference between the voltage and current in the circuit. I know it's given by tan^-1(im(z)/re(z)) but how do I do it here as the expression is a fraction?

 

[berkeman]

Is this question for schoolwork?

 

[Tesla In Person]

Is this question for schoolwork?

no.

 

[Tesla In Person]

Is this question for schoolwork?

I'm doing this question to prepare for exams but i got stuck here. Because it's not in standard complex form, i don't know how to find angle theta. I could rationalize the denominator but i might end up with a messier expression.

 

[berkeman]

Since it is related to schoolwork, I'll move this thread to the schoolwork forums for you now.

Does this reference help? https://www.electronics-tutorials.ws/accircuits/parallel-circuit.html

 

[Gavran]

The impedance is expressed as a reciprocal of a complex number. All you need to do is the next: $z=\frac{1}{a+bj}=\frac{a}{a^2+b^2}+\left(-\frac{b}{a^2+b^2}\right)j$ (https://en.wikipedia.org/wiki/Multiplicative_inverse#Complex_numbers).