A diagram of an alternating current (AC) electric circuit is shown along with the impedance (measured in ohms, Ω) of each component in the circuit. An AC power source, which is shown on the left in the diagram and labeled 120 V (for volts), causes electrons to flow through the circuit. Impedance is a measure of each component’s opposition to the electron flow. 1-Using the picture and chart above find the impedance of the Resistor.

2-Using the picture and chart above find the impedance of the Inductor.

3-Using the picture and chart above find the impedance of the Capacitor.

4-Find the total Impedance (sum of all parts together).

Part III: Ohm’s law for AC electric circuits says that the voltage V (measured in volts) is the product of the current I (measured in amps) and the impedance Z (measured in ohms): V = I ∙ Z. For the given circuit, the current I is 24 + 12i amps. What is the voltage V for each component in the circuit? Remember that Z is the impedance of each part from Part I.
1- What is the Voltage of the Resistor?

2- What is the Voltage of the Inductor?

3- What is the Voltage of the Capacitor?

4- What is the Total Voltage?

Part IV: Now that you understand the works of a simple electrical circuit, an electrical engineer student needs your assistance. Since it has been years since he has seen a complex number he has forgot the concept of imaginary numbers and how to perform operations on complex numbers. Your task is to write a letter to this student expressing your knowledge on that topic. In this letter you must include what an imaginary number is, where it comes from, and why it is needed. You must also explain what a complex number is and how to perform basic operations with them. I want you to also discuss the type of numbers your answers will be when you add, subtract, or multiply complex numbers. Your letter will be graded on the depth of your knowledge of material. I am looking for a professional, grammatically correct, letter. You must turn this sheet with your math work completed on it as well as your letter attached to it.