Complex Numbers Add Subtract Multiply and Divide Addition

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

• 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.

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

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

• 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

• Example 5:

• Example 6:

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

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

• Example 7: Complex Number Complex Conjugate

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

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

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

• Example 9: