1. 1.3(M2) Warm Up (8 + 4i) – (9 – 2i) (-2 – i) + (-6 – 3i)

2. Daily Assessment 6 – (-3 + 8i) + 5i (8 + 11i) + (25 + 28i)

3. 1.3 Multiply and Divide Complex Numbers

4. Vocabulary
To multiply two complex numbers, use the distributive property or the FOIL method just as you do when multiplying algebraic expressions.
Remember that i=√-1 so 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.

5. Examples
1. 6i(-3–7i) 2. (2+4i)(2-6i)

6. Try these . . .
6i(2 – 4i)
(6 – 3i)(2 + 5i)
(3 – 8i)²

7. To Divide Complex Numbers:
Rationalize the denominator by multiplying by the conjugate.
Examples:

8. EXAMPLE 5
Divide complex numbers
Write the quotient in standard form.
7 + 5i
1  4i

9. Write the expression as a complex number in standard form.5
1 + i d.
i(9 – i) e.
(3 + i)(5 – i) g.
5 + 2i f.
3 – 2i

10. Try these . . .