What is $\vert 2+i \vert$? 1. $1$ 2. $\sqrt{3}$ 3. $5$ 4. $\sqrt{5}$ 5. Something else! Note: * Correct Answer: D * Use pythagoras in the complex plane

What is $(1+i)^2/(1-i)$? 1. $e^{i\pi/4}$ 2. $\sqrt{2}e^{i\pi/4}$ 3. $e^{i3\pi/4}$ 4. $\sqrt{2}e^{i3\pi/4}$ 5. Something else! Note: * Correct Answer: D * Best to convert to euler with phase and just use the rules for adding and subtracting of exponents

Which point below best represents $4e^{i3\pi/4}$ on the complex plane? <img src="./images/complex_numbers_graph.png" align="center" style="width: 600px";/> Note: * Correct Answer: D

What is $Re\left[\frac{e^{i\omega t}}{1+i}\right]$? 1. $\frac{1}{\sqrt{2}}\cos(\omega t + \pi/4)$ 2. $\frac{1}{\sqrt{2}}\cos(\omega t - \pi/4)$ 3. $\frac{1}2\cos(\omega t + \pi/4)$ 4. $\frac{1}2\cos(\omega t - \pi/4)$ 5. Something else Note: * Correct Answer: B

A resistor ($R$) and an inductor ($L$) are in parallel. What is the effective impedance, $Z_{eff}$ across these elements? 1. $R + L$ 2. $R + i\omega L$ 3. $1/(R+i\omega L)$ 4. $\dfrac{1}{1/R -i/(\omega L)}$ 5. Something else? Note: * Correct Answer: D

<img src="./images/RLC.png" align="right" style="width: 400px";/> What is the total impedance of this circuit, $Z_{total}$? 1. $R + i\left(\omega L + \frac{1}{\omega C}\right)$ 2. $R + i\left(\omega L - \frac{1}{\omega C}\right)$ 3. $\frac{1}{R} + \frac{1}{i\omega L} + {i \omega C}$ 4. $\dfrac{1}{\frac{1}{R} + \frac{1}{i\omega L} + {i \omega C}}$ 5. None of these Note: * Correct Answer: B

AC voltage $V$ and current $I$ vs time $t$ are as shown: <img src="./images/IV_graphs.png" align="center" style="width: 600px";/> The graph shows that.. 1. $I$ leads $V$ ( $I$ peaks before $V$ peaks ) 2. $I$ lags $V$ ( $I$ peaks after $V$ peaks ) 3. Neither Note: * Correct Answer: B