AC Circuits: Solving for Impedance and Voltage in Complex Notation

[Calpalned]

Homework Statement

Homework Equations

$a + bi$ complex notation
Rules of resistors given in part b
b = imaginary part

The Attempt at a Solution

For part (a) how do I rewrite I(t) as a + bi?
For part (b) I need a formula that equates Z to R.
For part (c) do I simply write b (from part a)?
For part (d) what does the tilde on V = IZ mean? Is the I complex?
For part (e) how can I find a real voltage if I've only been working with imaginary ones?
For part (f) I would naturally take the derivative of I, set it equal to zero to find a maximum? I know that if |V| = constant C, then V = +C and V = -C. How does this apply to the problem?

My teacher said that this is an applied math course (mathematical physics) but that we don't have to know physics, just be able to solve math. Additionally, I hope I am not breaking the policy of not asking more than one question, (this question has 6 parts).

Thank you.

 

[andrewkirk]

It looks like the problem has supplied most of the formulas you need, but not all of them.

To do part (a) you need the formulas for impedance of a capacitor and an inductor, as well as of a resistor. The formulas are here. Note that $j$ is used in electrical calcs for $\sqrt{-1}$, rather than the $i$ that is used elsewhere in maths.

To do (b), use the results for the different impedances Z you got in (a), together with the formulas given in the first line of (b) for adding impedances in series and in parallel. Internet search 'series parallel circuit' if you don't know what 'series' and 'parallel' mean.

See how you go with that and whether you build up enough momentum to finish the problem. If not, show what you've managed to do, and further hints may be suggested.