Complex Numbers

Class Opener:

Quiz:

• 13 multiple choice questions

• Input answers in on the clicker

• Should be very easy.

ACT Class Opener:

• http://sbstjohn.com/QODWebSite/PlaneGeom/plane_1213_f016.htm

• http://sbstjohn.com/QODWebSite/PlaneGeom/plane_1213_f068a.htm

• http://sbstjohn.com/QODWebSite/Trigonom/trig_1213_f015.htm

Re-Do

• Partner Up and re-do the top 5 missed questions from the quiz yesterday.

7 ,8, 9, 12, 13

Class Opener:

Definition of pure imaginary numbers:

Any positive real number b,

where i is the imaginary unit and bi is called the pure

imaginary number.

b2 b2 1 bi

Definition of pure imaginary numbers:

i 1

i2 1

i is not a variable it is a symbol for a specific

number

Simplify each expression.

1. 81 81 1 9i

2. 121x5 121x4 1 x 11x2i x

3. 200x 100 1 2x 10i 2x

4. 8i 3i 24i2 241

Remember i2 1

Simplify each expression.

24

5. 5 20 i 5i 20Remember that 1 i

i2 100 110Remember i

2 1

10

i0 1

Cycle of "i"

i1 i

i2 1

i3 i

i4 1

i5 i

i6 1

i7 i

So i12 i0

i12

Simplify.

To figure out where we are in the cycle divide the exponent by 4 and look at

the remainder.

124 =3 with remainder 0

1

So i17 i1

Simplify.

Divide the exponent by 4 and look at the

remainder.

174 =4 with remainder 1

i

i17

So i26 i2

Simplify.

Divide the exponent by 4 and look at the

remainder.

264 =6 with remainder 2

1

i26

So i11 i3

Simplify.

Divide the exponent by 4 and look at the

remainder.

114 =2 with remainder 3

i

i11

Definition of Complex Numbers

Any number in form a+bi, where a and b are

real numbers and i is imaginary unit.

Definition of Equal Complex Numbers

Two complex numbers are equal if their real parts are equal and their imaginary

parts are equal.If a + bi = c + di,

then a = c and b = d

When adding or subtracting complex numbers, combine like terms.

Ex: 8 3i 2 5i 8 2 3i 5i

10 2i

8 7i 1211i

8 12 7i 11i

418i

Simplify.

Simplify.

9 12 6i 2i

3 8i

9 6i 122i

Multiplying complex numbers.

To multiply complex numbers, you use the

same procedure as multiplying polynomials.

Simplify.

8 5i 2 3i

16 24i 10i 15i2F O I L

16 14i 15 31 14i

Simplify.

3018i 10i 6i2F O I L

3028i 6 2428i

62i 5 3i

The Habitat for humanity project utilizes volunteers to help build house for low – income

families who might not be able to afford the purchase of a home. At a recent site, Habitat workers built a small storage shed attached to

the house. The electrical blueprint for the shed called for two AC circuits connected in series with a total voltage of 220 volts. One of the

circuits must have an impedance of 7-10j ohms, and the other needs to have an impedance of 9+5j ohms. According to the building codes,

the impedance cannot exceed 20-5j ohms. Will the circuits, as designed, meet the code?

Complex Conjugates:

Multiplying Conjugates

• Multiply (3 – 5i) by its complex conjugate.

Student Check:

Quotient of Complex Numbers

Student Check:

Graphing Complex Numbers:

• How do we graph the following:

1.2 + 3i2.-1 + 2i3.-3i

Student Practice:

• Pg. 137 – 138 • #1 – 76 odd

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