1. College Algebra Chapter 1 Equations and Inequalities
Section 1.3
Complex Numbers

2. 1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi
3. Perform Operations on Complex Numbers

3. Simplify Imaginary Numbers
and
If b is a positive real number, then

4. Examples 1 – 4:
Write each expression in terms of i and simplify: 1. 2. 3. 4.

5. Examples 5 – 7:
Write each expression in terms of i and simplify: 5. 6. 7.

7. Example 8:
Multiply

8. Example 9:
Multiply

9. Example 10:
Divide

11. 1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi
3. Perform Operations on Complex Numbers

12. Write Complex Numbers in the Form a + bi
Given real numbers a and b, a number written in the form a + bi is called a complex number.
a is the real part
b is the imaginary part

13. Examples 11 – 13:
Simplify and write the result in standard form a + bi. –5 i
13.

14. Examples 14, 15:
Simplify and write the result in standard form a + bi.
14.
15.

16. 1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi
3. Perform Operations on Complex Numbers

17. Perform Operations on Complex Numbers
Powers of i :
Every fourth power of i equals 1.

18. Perform Operations on Complex Numbers
To simplify a power of i, write the expression as i to a power of 4 multiplied by

19. Examples 16 – 18:
Simplify:
16.
17.
18.

21. Perform Operations on Complex Numbers
To add or subtract complex numbers,
add or subtract their real parts,
and add or subtract their imaginary parts.

22. Examples 19, 20:
19.
20.

24. Perform Operations on Complex Numbers
Multiply complex numbers as you would multiply polynomials.
Remember

25. Example 21:

26. Example 22:

28. Example 23:

29. Example 24:

31. Perform Operations on Complex Numbers
The expressions a + bi and a – bi are called complex conjugates.
The product of complex conjugates is a real number.

32. Perform Operations on Complex Numbers
To divide complex numbers, make the denominator a real number so the quotient can be written in the form a + bi.

33. Example 25:
Divide and write the result in the form a + bi.

34. Example 26:
Divide and write the result in the form a + bi.

35. Example 27:
Divide and write the result in the form a + bi.

36. Example 28:
Divide and write the result in the form a + bi.