In this lesson we are going to take a look at complex number. You'll learn some new vocabulary, and get familiar with imaginary numbers, complex numbers, and their real and imaginary part. The imaginary number i is defined as the square root of -1. This can be used to re-write square roots of any negative number. Also, the imaginary number is a part of a complex number, which is defined as a combination of a real and imaginary part. To add or subtract complex numbers think of adding like terms. You'll also learn how to multiply and divide complex numbers. Finally, you'll see how to simplify powers of i, and some shortcuts for simplifying these powers.
The imaginary number i is defined as the square root of -1. This can be used to re-write square roots of any negative number.
A complex number is a number of the form a + bi. Here a is the real part and b the imaginary part.
To add or subtract complex numbers think of adding like terms.
To multiply complex numbers think of multiplying using FOIL. Note that any i2 simplifies to -1.
To divide by a complex number, multiply the top and bottom by the complex conjugate of the denominator.
Higher powers of i can be simplified into an expression that no longer has a power. One method involves dividing the power by four and checking the value of the remainder.
Remainder of 1 simplifies to i
Remainder of 2 simplifies to -1
Remainder of 3 simplifies to –i
Remainder of 0 simplifies to 1
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.