Lesson 1.3.1: Defining Complex Numbers, , and

By the end of this lesson, I will be able to answer the following questions… 1. How are complex numbers and real numbers related? 2. How do we rewrite radicals in imaginary units (and back)? 3. How do we rewrite higher powers of imaginary units using and ? 4. How are imaginary number used in applications involving electricity?

Vocabulary Imaginary Unit Complex Number Volts: refers to the energy Standard Form Volts: refers to the energy that could be released if electric current is allowed to flow. Amperes: are used to express flow rate of electric charge. Impedance: resistance of an electric circuit or component to alternating current

Prerequisite Skills with Practice Simplify the following radicals (not using a calculator.) I your own words, explain why

Example one Identify the real and imaginary parts of the complex number: Example two Rewrite the complex number 2i using a radical. Example three Rewrite the radical using the imaginary unit i. GeoGebra Example Three

Example four Simplify GeoGebra Example Four Example five Complex numbers are used to represent the impedance of an element in a circuit. The voltage, V, is the real part of the complex number, and the current, I, is the coefficient of the imaginary unit i. So, impedance is equal to V + Ii, where I is in milliamperes. A certain element has a voltage of 18 volts and a current of 2 milliamperes. Use a complex number to represent the element’s impedance.