1. Lesson 1.3.1: Defining Complex Numbers, , and

2. 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?

3. 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

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

5. 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

6. 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.