COMPLEX NUMBERS
CHAPTER 1: COMPLEX NUMBERS AND THE IMAGINARY UNIT
A. THE IMAGINARY UNIT i
B. POWERS OF THE IMAGINARY UNIT
C. COMPLEX NUMBERS
D. EQUATIONS WITH IMAGINARY ROOTS
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CHAPTER 2: COMPLEX NUMBERS AND THE COMPLEX PLANE
A. THE COMPLEX PLANE
B. CONJUGATE OF A COMPLEX NUMBER
C. BASIC OPERATIONS IN C
1. Addition and Subtraction
2. Multiplication
3. Properties of Addition and Multiplication
4. Division
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D. MODULUS OF A COMPLEX NUMBER
E. DISTANCE BETWEEN TWO COMPLEX NUMBERS
F. LINES AND CIRCLES IN THE COMPLEX PLANE
–The Colors of Infinity
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CHAPTER 3: POLAR COORDINATES
A. THE POLAR COORDINATE SYSTEM
B. GRAPHING POLAR EQUATIONS (OPTIONAL)
C. RELATION BETWEEN THE POLAR AND RECTANGULAR COORDINATE SYSTEMS
1. Converting Between Polar and Rectangular Coordinates
2. Relation Between Polar and Rectangular Equations
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CHAPTER 4: POLAR REPRESENTATION OF COMPLEX NUMBERS
A. POLAR FORM OF A COMPLEX NUMBER
B. BASIC OPERATIONS ON COMPLEX NUMBERS IN POLAR FORM
1. Addition and Subtraction
2. Multiplication and Division
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C. POWERS OF A COMPLEX NUMBER
–Equiangular Spirals
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D. ROOTS OF A COMPLEX NUMBER
1. nth Roots of a Complex Number
2. Square Roots of a Complex Number
3. Cubic Roots of a Complex Number
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E. LOCI OF COMPLEX NUMBERS WITH A COMMON ARGUMENT
F. ROTATIONS IN THE COMPLEX PLANE
–The Greatest Equation Ever