Presentation on theme: "Table of Contents Complex Numbers – Add, Subtract, Multiply, and Divide Addition of complex numbers is given by: Example 1:"— Presentation transcript:
Table of Contents Complex Numbers – Add, Subtract, Multiply, and Divide Addition of complex numbers is given by: Example 1:
Table of Contents 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.
Table of Contents Subtraction of complex numbers is given by: Example 3:
Table of Contents Again, not all the steps were necessary, and learning to work the problem quickly in your head is good. Example 4:
Table of Contents 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
Table of Contents Example 5:
Table of Contents Example 6:
Table of Contents Consider the complex number The Complex Conjugate of this number is given by: Notice what happens when you multiply complex conjugates.
Table of Contents Notice the difference between multiplying complex conjugates and multiplying binomials as in previous work. Complex Conjugate Binomials When multiplying complex conjugates, remember the + sign!
Table of Contents Example 7: Complex Conjugate Complex Number
Table of Contents To compute the Division of complex numbers, multiply both the numerator and the denominator by the complex conjugate of the denominator.
Table of Contents Example 8:
Table of Contents The problem is not complete at this point. Always express complex number answers in a+bi form.