RC circuit question

[tjr39]

1. The problem statement, all variables and given/known data

Given an RC circuit which has a Capacitor (C=6\times 10^{-6} F) and a resistor (R=5 \Omega) conected in series to an a.c. voltage sorce of the form v=V_{0} e^{j\omega t} with a V_{0}=1 Volt. Frequency f=10kHz
a)What is the phase of the current with respect to the applied voltage?
b) What is the magnitude of the current?

2. Relevant equations

Z=Z_{R}+Z_{C}

Z_{C}=\frac{1}{j\omega C}

Z=x+jy where j=\sqrt{-1}

Z=ze^{j \phi} with z=\sqrt{x^{2}+y^{2}} and \phi =tan^{-1} \frac{y}{x}

\omega = 2\pi \times f

3. The attempt at a solution

\frac{1}{\omega C} = 2.65

Z=R+ \frac{1}{j\omega C}

=5-2.65j

Which can be written as Z=ze^{j\phi}

z=\sqrt{5^{2}+2.65^{2}}=5.66

\phi =tan^{-1}\frac{-2.65}{5}=-27.9 degrees

Since i=\frac{V_{0}}{z}e^{j(\omega t-\phi)} then I can say the current leads the voltage by 27.9 degrees.

And I can also say the magnitude of the current i is equal to \frac{V_{0}}{z}=\frac{1}{5.66}

How did I go?? Am I on track anywhere at all or have I made a bit of a mess of it?
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution