Course Materials
Lessons
Complex Conjugates
- Video - Conjugate Pairs of Complex Numbers (3:54)
- Topic - Writing Conjugate Pairs of Complex Numbers
- Topic - Writing Conjugate Pairs of Complex Numbers using Notation
- Topic - Proof using Conjugate Pairs 1
- Topic - Proof using Conjugate Pairs 2
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 1
- Topic - Quadratic Equations with Real Coefficients Having Complex Roots 2
Conjugates and Division of Complex Numbers
- Video - Realising the Denominators using Conjugate Pairs (6:28)
- Video - Proof regarding Conjugate Pairs (4:13)
- Video - Proof regarding Conjugate Pairs & Realising Denominators (2:20)
- Topic - Division of Complex Numbers 1
- Topic - Division of Complex Numbers 2
- Topic - Multiplicative Inverse of Complex Numbers 1
- Topic - Multiplicative Inverse of Complex Numbers 2
Modulus
- Topic - Modulus of Complex Numbers
- Topic - Modulus of Purely Imaginary Complex Numbers
- Topic - Modulus of Purely Real Complex Numbers
- Topic - Modulus of Conjugate Pairs
- Topic - Modulus of Polar Form
- Topic - Proof Regarding Modulus
- Topic - Proof Regarding Modulus and Conjugate Pairs
- Topic - Modulus Squared and Multiple of Complex Number and its Conjugate
- Topic - Finding Modulus by Polar Form
Equations over Complex Number Field
- Video - Complex Roots of Quadratic Equations (4:06)
- Video - Complex Roots of Cubic Equations (2:35)
- Video - Complex Roots of Quadratic Equations using Quadratic Formula (4:19)
- Video - Quadratics in Complex Number Field using Quadratic Formula (2:41)
- Video - Quadratics in Complex Number Field using Completing Square (7:54)
- Video - Square Roots of Complex Numbers using Factorise Method 2 (5:33)
Modulus-Argument (Polar) Form
- Video - Understanding Modulus-Argument Form (8:13)
- Topic - Horizontal Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Vertical Complex Numbers to Modulus-Argument (Polar) Form
- Topic - First Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Second Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Third Quadrant Complex Numbers to Modulus-Argument (Polar) Form
- Topic - Fourth Quadrant Complex Numbers to Modulus-Argument (Polar) Form
Conversion between Cartesian and Polar Forms
- Video - Complex Numbers in 1st Quarter to Mod-Arg Form (4:26)
- Video - Complex Numbers in 2nd Quarter to Mod-Arg Form (2:33)
- Video - Complex Numbers in 4th Quarter to Mod-Arg Form (4:29)
- Video - Complex Numbers in Purely Real to Mod-Arg Form (2:23)
- Video - Complex Numbers in Purely Imaginary to Mod-Arg Form (1:47)
- Video - Modulus-Argument Form to Cartesian Form (5:38)
- Video - Mod-Arg Form to Cartesian Form in Pure Real or Imaginary (4:23)
- Video - Simplifying Complex Numbers using Mod-Arg Form (3:45)
- Video - Exact Values of Sine & Cosine using Mod-Arg Form (4:57)
De Moivre's Theorem
- Video - Understanding De Moivre's Theorem (2:44)
- Video - Proof of De Moivre's Theorem Multiplication (3:42)
- Video - Proof of De Moivre's Theorem Division (2:20)
- Video - Proof of De Moivre's Theorem Subtraction (4:04)
- Video - Simplifying Complex Numbers using De Moivre's Theorem (7:42)
- Video - Purely Imaginary using De Moivre's Theorem (5:11)
- Video - Purely Real using De Moivre's Theorem (5:24)
- Video - Trigonometric Expression using De Moivre's Theorem (5:27)
- Video - De Moivre's Theorem involving Conjugate Pairs (6:58)
- Video - Trigonometric Properties & De Moivre's Theorem (6:04)
Roots of Unity in Complex Numbers
- Video - Nth Roots of Unity using Complex Numbers (8:04)
- Video - Complex Roots of Unity (6:03)
- Video - 4th Roots of Unity using Complex Numbers (3:09)
- Video - 5th Roots of Unity using Complex Numbers (1:57)
- Video - 6th Roots of Unity using Complex Numbers (2:30)
- Video - Cube Roots of Negative Unity using Complex Numbers (2:09)
- Video - Seventh Root of Unity (6:46)
Roots of Complex Numbers
- Video - 4th Roots of 4 using Complex Numbers (2:32)
- Video - 5th Roots of -32 using Complex Numbers (2:45)
- Video - Cube Roots of i using Complex Numbers (2:19)
- Video - 4th Roots of -16i using Complex Numbers (1:42)
- Video - 5th Roots of 1+i using Complex Numbers (2:07)
- Video - Cube Roots of Irrational Real Part & i using Complex Numbers (1:30)
- Video - Exact Values of Trigonometric Ratios involving Fifth Roots (6:37)
