1. 3.3: Complex Numbers Objectives: • Define “complex” numbers
• Perform operations with
complex numbers.

2. Concept: Solution to Quadratics
RECALL: A solution to a system of
of equation is the point
where the two equations
intersect.
A solution to a quadratic or any other function is the point(s) where the graph of the equation crosses the x –axix.
These are also known as roots, and x-intercepts.

3. Concept: Solution to Quadratics
An imaginary number occurs when the graph of a quadratic function does not cross the x–axis. There is NO REAL SOLUTION.

8. Concept: Powers of i cont. . .
Whenever the exponent is
greater than 4, you can
use the fact that i4 = 1
to find the value.

9. Concept: Powers of i cont. . .
1. Divide the exponent by 4:
Rewrite I using the remainder as the exponent.
Solve. Use your chart from
these notes.

11. You Try:
5i – 7 + 2i – 8i
Solution: –i – 7

12. Concept: Multiplying Complex Numbers
Ex: (3i + 2)(5i – 6)
5i – 6
Use the box method
to multiply binomials. 3i 2
15i2
–18i
10i
–12
2. Write the equation.
15i2 –18i + 10i – 12
15i2 – 8i – 12
15(–1) – 8i – 12
3. Replace i2 with –1
–15 – 8i – 12
4. Simplify if possible.
– 8i – 27