Complex Numbers

Complex Numbers

Let's see what we already know about this topic...

Open Ended

 What is the value of $i$ ? Not sure? Take a guess.

Multiple Choice

A complex number is written as $a+bi$ . What part of the expression is considered the imaginary part? 

•  $a$  

•  $b$  

•  $bi$  

•  $i$  

Some Properties of Complex Numbers

• Complex numbers are plotted on a plane called the Argand plane.

• They're plotted based on (a,b) coordinates

• The value of $i=\sqrt{-1}$  

• This means that the value of  $i^2=-1$  

Operations with Complex Numbers

• When adding and subtracting, real parts stay with real parts and imaginary parts stay with imaginary parts.

The Modulus of a Complex Number

• The modulus is the term used for complex numbers to describe their absolute value.

•  $\left|z\right|=\sqrt{a^2+b^2}$  

What's this All leading to anyway?

• Understanding complex numbers also allows us an understanding into how polar coordinates are formed.

• The idea of complex roots shows that zeroes can exist outside of what we see graphically and that the realm of numbers isn't limited to the concrete.