1. Section 5.9.B
Complex Numbers

2. Def: A complex number is any number that can be
written in the form a + bi, where a and b are real
numbers and i is the imaginary unit.
a + bi
Real part
Imaginary part
Some answers can be just the imaginary part

3. The Complex Number System (a + bi)
real numbers
(b = 0)
imaginary numbers
(b ≠ 0)
rational numbers
irrational numbers
pure imaginary
(a = 0)
non-pure imaginary
(a ≠ 0)

4. Def: Two complex numbers are equal if their real parts
are equal and if their imaginary parts are equal
10.) Solve for x and y
3x + 10i = yi
Set real parts equal and imaginary parts equal then solve
real
imaginary
3x = 12
10i = 5yi
x = 4
10 = 5y
y = 2

5. add the imaginary parts
Adding and Subtracting Complex Numbers
Add the real parts
and
add the imaginary parts
11.) Add: (2 + 3i) + (6 - 4i)
12.) Subtract: (9 - 3i) - (6 + 2i)

6. http://www.youtube.com/watch?v=htiloYIILqs 13.) Multiply 2i(5i2 + 3i)
Multiplication of imaginary numbers
13.) Multiply 2i(5i2 + 3i)
= 10i3 + 6i2
= 10•i2•i + 6i2
Replace the i2 with -1
= 10(-1)i + 6(-1)
Standard form a + bi
= i

7. 14.) Multiply: -3i(5 + 4i)
but….. i2 = -1
15.) Multiply: (3 - 2i)(-1 + 3i)

8. 16.) Multiply by the conjugate:
FOIL

9. In-class assignment Homework Practice 5-9 Problems: 9-24 all
Page 315 # all
Homework