You throw away the outside and cook the inside.

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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

Check Homework

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.

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

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:

1

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

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

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

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.

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

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!

Classwork: Worksheet: 3.4 & 3.5