Advanced Complex Numbers and Roots

📋 Course Outline

1. Complex numbers: modulus, argument and conjugate
2. Cube roots and fourth roots of unity
3. Complex numbers in polar form and trigonometry
4. Functions: types, graphs and periodicity
5. Sequences and series: arithmetic and geometric
6. Factorials, permutations and combinations
7. Partial fractions and synthetic division
8. Trigonometric identities and allied angles
9. Limits and continuity with derivatives
10. Vectors: magnitude, dot and cross products

📖 1. Complex numbers: modulus, argument and conjugate

🔑 Key Concepts & Definitions

• Modulus of a complex number : Modulus is the non-negative distance of a complex number from the origin in the complex plane.
• Argument of a complex number : Argument is the angle a complex number makes with the positive real axis in the complex plane.
• Complex conjugate : Complex conjugate is formed by changing the sign of the imaginary part of a complex number.
• Polar form : Polar form expresses a complex number using its modulus and argument as $r(\cos\theta+i\sin\theta)$.

📝 Essential Points