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The Complex Number The Arithmetic of Complex Numbers Simplify expressions using IMAGINARY NUMBERS.
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Section 1.5 Day 1– Complex Numbers
After this section you should be able to:
• Simplify expressions using IMAGINARY NUMBERS.
The Imaginary Number 1 i
4 2i 16 4i 7 i 7 81 9i
The Arithmetic of Imaginary Numbers
2 32 3 4
41 i i 1 i i i1 1 11
2i 3i5i
7i 9i2i
4i 3i212i
12
i 4i 2i38i
8i
3ii
336i
2i 3
4i
ii
2
4ii
4i
2
5ii
5i1
5i
• Simplify expressions using IMAGINARY NUMBERS.
The Complex Number a biThe Arithmetic of Complex Numbers
2 3i 3 5i
5 2i
7 i 2 3i
5 4i
2i 4 9i28i 18i
18 8i
2 3i 1 4i 22 8i 3i 12i
2 8i 3i 12 14 5i
5 i 2 7i 210 35i 2i 7i
10 35i 2i 7 17 37i
6 7ii i
i
2
2
6i 7ii
6i 7
1
6i 7
2 3i4 i
4 i4 i
2
2
8 2i 12i 3i16 i
8 2i 12i 316 1
5 14i17
5 14i17 17
• Simplify expressions using IMAGINARY NUMBERS.
5 2i2 i
2 i2 i
2
2
10 5i 4i 2i4 i
10 5i 4i 2
4 1
12 1 i5 5
7 6ii i
i
2
2
7i 6ii
7i 61
6 7i
1 i1 i
1 i1 i
2
2 2
1 i i i1 i
1 i i 12
i
14
7
2ii
72i 4 32 i i 2 1 i 2i
2
5
4ii 3
4i
4i
ii
2
4ii
4i
9 i3i i
i
2
2
9i i3i
9i 13
1 3i3
• Simplify expressions using IMAGINARY NUMBERS.
Section 1.5 Day 1 – Complex Numbers
Homework: Pg. 129 #5-14,17-22, 31-34, 37-40
After this section you should be able to:
• Simplify expressions using IMAGINARY NUMBERS.
• Solve quadratic equations using IMAGINARY NUMBERS.
Section 1.5 Day 2– Complex Numbers
After this section you should be able to:
• Solve quadratic equations using IMAGINARY NUMBERS
Given the quadratic equation below:A) Compute the value of the discriminant.B) Determine the number of real solutionsC) Solve the quadratic equation (if possible)
2x 3x 8 0
2A) 3 4 2 8 23
B) Zero real solutions
3 23C)2
2x 16 0
2A) 0 4 1 16 64
B) Zero real solutions
2C) x 16
x 16
Complex Numbers and the Quadratic Formula
X
3 i 232
x 4i
• Solve quadratic equations using IMAGINARY NUMBERS.
Given the quadratic equation below:A) Compute the value of the discriminant.B) Determine the number of real solutionsC) Solve the quadratic equation
22x 2x 1 0
2A) 2 4 2 1 12
B) Two real solutions
2 12C)4
2x 3x 5 0
2A) 3 4 1 5 11
B) Zero real solutions
3 11C)2
3 i 112
2 2 3 1 34 2
• Solve quadratic equations using IMAGINARY NUMBERS.
Section 1.5 – Complex Numbers
Homework:
After this section you should be able to:
Pg. 129 #49-53, 63-66
• Simplify expressions using IMAGINARY NUMBERS.
• Solve quadratic equations using IMAGINARY NUMBERS.
