1. Complex Numbers Imaginary Numbers Vectors Complex Numbers
Add or Subtract Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers

2. Imaginary Numbers Key Point:
Imaginary numbers are numbers that result from taking the square root of negative numbers.

3. Vectors
Key Point:
A vector is a line drawn from the origin to some given point.
In electronics we call a vector a phasor.
Graphically, the operator j rotates a phasor 90°.

4. Complex Numbers Key Point:
Complex numbers are numbers that are part real and part imaginary.
4 + j3

5. Add or Subtract Complex Numbers
Key Point:
To add (or subtract) complex numbers,
first add (or subtract) the real parts, then add (or subtract) the imaginary parts.
(‑9+j6)+(12‑j2)
=3+(j6‑j2) =3+j4

6. Multiplying Complex Numbers
Key Point:
Complex numbers are multiplied the same way we multiply algebraic terms.
(2 + j3)(2 + j4)
= 4 + j6 + j8 + j212
= 4 + j14 + (‑1)12
= ‑8 + j14

7. Dividing Complex Numbers
Key Point:
To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator. This will remove the imaginary part from the denominator.