1. Connections - Unit H - Complex Numbers
Friday, April 8
Complex Numbers
Define and use imaginary and complex numbers.

2. Complex Numbers
You can see in the graph of f(x) = x that f has no real zeros.
However, you can find solutions if you define the square root of negative numbers, which is why imaginary numbers were invented.
The imaginary unit i is defined as
FHS
Quadratic Function

3. Complex Numbers
A complex number is written in the form a + bi where a and b are real numbers and i is the imaginary unit.
For two complex numbers to be equal both a’s and both b’s must be equal.
All numbers are complex numbers.
Real numbers (the numbers we normally deal with) would be those where b is equal to 0.
FHS
Quadratic Function

4. Imaginary Numbers
An imaginary number is written in the form a + bi, where b is a real number ≠ 0 and a can be equal to 0 or not.
Since you can factor out a -1 from any negative number and then express the square root of a negative number as an imaginary number.
FHS
Quadratic Function

5. Examples Simplify the following. Express the numbers in terms of i.
FHS
Quadratic Function

6. Examples Find the values of x and y that make each equation true FHS
Quadratic Function