The document provides examples of multiplying different types of complex numbers: (1) a real number times a complex number changes the length of the vector; (2) multiplying by -1 rotates the vector 180 degrees; (3) multiplying by i rotates the vector 90 degrees; (4) multiplying two complex numbers uses the distributive property; and (5) multiplying conjugates results in the real part being the product of the real parts and the imaginary part being the negative product of the imaginary parts.

1. Previous Practice:
Example 1: 5(2 + 3i)
multiply by real
number:
changes length
Example 2: -2(3 - 4i) of vector
10+15i
multiply by ­1: rotate 180
1

2. Imaginary Number x Complex Number
Example 1: i(3 + 4i)
Example 2: 4i(2 - 3i)
multiply by i:
rotate 90
2

3. Complex Number x Complex Number
Example 1: (5 + 3i)(2 + 4i)
Example 2: (-2 + 5i)(3 - i)
3

4. Multiplying Conjugates
Example 1: (3 + 2i)(3 - 2i)
Example 2: (-5 - i)(-5 + i)
4

5. General Rule When Multiplying Conjugates:
(a + bi)(a - bi) =
5