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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
• Skip Vocabulary Section
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