2.2 Complex Numbers

1. Principle Square root
2. sq. root(a.b) = sq. root(a) * sq. root(b), iff a and b both are not negative
3. Complex Number => i^2^ = - 1

• Real part
• Imaginary part
• Principle Square Root

4. Complex Plane

• The horizontal number line (what we know as the xxx-axis on a Cartesian plane) is the real axis.
• The vertical number line (the yyy-axis on a Cartesian plane) is the imaginary axis.

5. Number Systems

• Counting number system ( greater than 0)
• Integer number system (positive and negative numbers)
• Rational number system (fractions)
• Real number system (decimals)
• Complex number system

6. Pure imaginary
7. Adding and subtracting complex numbers
8. Multiplying complex number
9. (a - bi)(a+bi) = a^2^+b^2^Imaginary Numbers

Imaginary Numbers are Real

1. Introduction
2. History
3. Cardan's Problem
4. Bombelli's Solution
5. Numbers are Two Dimensional
6. The Complex Plane
7. Comple Multiplication
8. Math Wizardry
9. Closure
10. Complex Functions
11. Wandering in 4 Dimensions
12. Riemann's Solution
13. Riemann Surfaces