1.3Multiplying and Divide

Complex Numbers

1.1-1.3 Quiz: Thursday

Vocabulary

• To multiply two complex numbers, use the FOIL method.– REMEMBER: i2 = -1

• Two complex numbers of the form (a + bi) and (a – bi) are called complex conjugates. – The product of complex conjugates is always a real

number.– Ex: (2 + 4i)(2 – 4i) = 4 – 8i + 8i + 16 = 20

Vocabulary• Complex Conjugates

– You can use this fact to divide complex numbers.

– When a quotient has an imaginary number in the denominator, multiply by the conjugate so that you have a real number in the denominator.

– Ex: what would we multiply by to get rid of the imaginary # in the denominator?

8 3

1 2

i

i

Example 1:

• Multiply the complex conjugates

1. (4 + 3i)(4 – 3i)

2. (8 – 4i)(8 + 4i)

Example 2:

• Write the expression as a complex number in standard form.

1. 4i(6 + 2i)

2. (3 – 2i)(-1 + 4i)

3. (5 + 7i)(2 + i)

Example 3:

• Write the expression as a complex number in standard form.

3 2

1 3

i

i

You Try:• Write the expression as a complex number

in standard form.1

2 3

6 4

4 5

i

i

i

i

Classwork

• Out of your notetaking guide

pg. 14-15 ALL