Transcript 1.3 Multiplying and Divide Complex Numbers

1.3
Multiplying 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  3i
1  2i
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  2i
1  3i
You Try:
• Write the expression as a complex number
in standard form.
1 i
2  3i
6  4i
4  5i
Classwork
• Out of your notetaking guide
pg. 14-15 ALL