1. You throw away the outside and cook the inside.
Lesson 3.4 & 3.5- Complex Numbers
& Complex Zeros
You throw away the outside
and cook the inside.
Then you eat the outside
and throw away the inside.
What did you eat?: 1.
corn
ANSWERS

2. Check Homework

6. PRE Lesson 3.4 & 3.5 Complex Number & Complex Zeros Objectives:
To understand complex numbers.
To add, subtract & multiply complex
numbers.
To solve equations with complex
numbers as solutions.

8. To reduce a power of i, just divide by 4 and the remainder will correspond to one of these.

11. Special care must be taken when performing
calculations involving square roots of negative
numbers. Although when
a and b are positive. This is not true when
both are negative. For example:

12. 1

14. Ex 2. Find all the zeros of the
1st Factor
2nd Solve each factor
3rd Use quadratic
formula
Ex 2. Find all the zeros of the
polynomial
A zero is given x=-3
So, a factor is
(x+3)
Use Synthetic Division
Factored
Use quadratic formula
Solutions

15. Ex 2. Find all the zeros of the
Again zeros are given x=-1
So, a factors are (x+1)(x+1)
Use Synthetic Division
Factored
polynomial continued
Ex 2. Find all the zeros of the
Remember, there are two factors of
(x+1)
Use Synthetic Division
Factored
Use quadratic formula
Solutions

16. Whenever a+bi is a zero, its complex conjugate a-bi is also a zero:

17. Ex 3. Find a polynomial with integer coefficients that have the given zeros.
We know it’s a degree of 3 a.k.a 3 zeros.
3a. Degree 3 and zeros 2 and 3-i.
One zero is 2 giving us a factor of (x-2).
Another zero is 3-i, so its conjugate 3+I is also a zero.

18. How did I get those funky factors?
To get a factor from x=2 we set it equal to zero.
In the same way I take the zero x=3-i and set it equal to zero.
Factor

19. Ex 3. Find a polynomial with integer coefficients that have the given zeros.
We know it’s a degree of 3 a.k.a 3 zeros.
3a. Degree 3 and zeros 2 and 3-i.
One zero is 2 giving us a factor of (x-2).
Another zero is 3-i, so its conjugate 3+I is also a zero.
Lastly, we multiply…everything!

20. Classwork: Worksheet: 3.4 & 3.5