1. Complex Numbers – Add, Subtract, Multiply, and Divide Addition of complex numbers is given by: Example 1:

2. It is good to leave out the middle step and to work the problem completely in your head. Example 2: It is perfectly fine to think of addition of complex numbers as adding binomials, but remember that i is not a variable, but an imaginary number.

3. Subtraction of complex numbers is given by: Example 3:

4. Again, not all the steps were necessary, and learning to work the problem quickly in your head is good. Example 4:

5. Multiplication of complex numbers is given by: It is often easier to think of multiplication of complex numbers using the foil pattern for binomials, even though these are numbers and not true binomials. Again, remember that i is not a variable, but an imaginary number

6. Example 5:

7. Example 6:

8. Consider the complex number The Complex Conjugate of this number is given by: Notice what happens when you multiply complex conjugates.

9. Notice the difference between multiplying complex conjugates and multiplying binomials as in previous work. Complex Conjugate Binomials When multiplying complex conjugates, remember the + sign!

10. Example 7: Complex Conjugate Complex Number

11. To compute the Division of complex numbers, multiply both the numerator and the denominator by the complex conjugate of the denominator.

12. Example 8: Divide: Determine the complex conjugate of the denominator Multiply both the numerator and denominator by the conjugate.

14. The problem is not complete at this point. Always express complex number answers in a+bi form.

15. Example 9: