1. 9-14-17 AM 2.3a To Simplify Complex Expressions
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This is a fractal. Complex numbers are used to generate fractals on the computer.

2. Active Learning Assignment?

3. * * Lesson: To simplify complex numbers
Complex numbers are in the form a + bi, where a is a real number and bi is the imaginary number. EVERY NUMBER CAN BE EXPRESSED AS A COMPLEX NUMBER.
How is “7” a complex number?
7 + ?i
7 + 0i
How is “2i” a complex number?
? + 2i
0 + 2i *
We know:
If we square both sides: *
Then: i2 = –1

4. * * * Property: * Property: Simplify in EXACT VALUE terms: Ex: Try:
What is the difference between these two?
* Property:
* Property:

5. Simplify in EXACT VALUE terms:
Try:

6. Ex:
Alternately:

7. Example:
{reduce}

8. Try:

9. Ex: (2 + 3i) + (5 – 4i)
{add real together and imaginary together}
i – 4i
7 – i
Ex: (5 – 2i) – (– 6 + 3i)
{add the inverse}
(5 – 2i) + ( i)
11 – 5i
Try: (7 – 9i) + (11 – i)
Try: (4 + 2i) – ( 7 – 2i)
18 – 10i
– 3 + 4i

10. Active Learning Assignment:
Facts About the Academy Awards Handout
(NO WORK – NO CREDIT! Show work on front or back, no extra paper, please.)