1. Complex Numbers

2. The imaginary unit i is defined as
Complex Numbers
The imaginary unit i is defined as

3. Example

4. Complex Numbers
The set of all numbers in the form a + bi with real numbers a and b, and i, the imaginary unit, is called the set of complex numbers.
The real number a is called the real part, and the real number b is called the imaginary part, of the complex number a + bi.

5. Equality of Complex Numbers
a+bi = c+di if and only if a = c and b = d

6. Adding and Subtracting Complex Numbers
Multiplying Complex Numbers

7. Example
Simplify:

8. Example
Multiply:

9. Conjugate of a Complex Number
The complex conjugate of the number a + bi is a - bi, and visa-versa. The product of a complex number and its conjugate is a real number.

10. Example
Rationalize:

11. Principal Square Root of a Negative Number
For any positive real number b, the principal square root of the negative number -b is defined by

12. Example
Simplify:

13. Quadratic Formula

14. Examples
Solve: