1. Conjugates Standard form of Complex Numbers

2. Standard form of a complex number
a + bi
a is real part bi is the imaginary part

3. Add or Subtract Addition
(3 + 4i ) + ( i ) = ( 3 + ( - 2))+(4 + 5) i
= 1 + 9i
Subtraction
(6 - 3i ) – (4 - 2i ) = (6 - 4) + (-3 – (- 2)) i
= 2 – i

4. Multiplication (a + bi)(c + di) ac + adi + cbi + bd(- 1)
ac – bd + (ad + cb) i
(4 + 3i)(5 – 2i)= 20 – 8i + 15i - 6(- 1)
26 + 7i

5. Multiply
(5 + 3i)(5 – 3i)

6. The complex numbers above are Conjugates
Multiply
(5 + 3i)(5 – 3i)
The complex numbers above are Conjugates

7. We use Conjugates to write Complex factions in standard form
Multiply the complex fraction by one. =
Important that it is
2 fractions
Standard form

8. Use the Quadratic formula to solve
8x2 -3x + 5 = 0

9. Homework
Page
# 3, 13, 19, 25,
29, 33, 38, 40,
45, 58, 62, 70,
78, 89, 99, 101

10. Homework
Page
# 6, 14, 23, 26,
31, 35, 39, 51,
57, 61, 69, 73,
83, 100