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.: Welcome to the Complex Numbers Tutorial

Complex numbers are numbers that consist of the imaginary number which represents a negative root.

Complex numbers consist of a number where and are real numbers and is the imaginary unit. The number is the real part of the complex number, and the number is the imaginary part.

Basically, with Complex numbers, you can define a negative root, since is equal to a negative root.

.: By Freddy Ieong Period 6

Complex, yes?

.: Adding and Subtracting Complex Numbers

In order to add or subtract complex numbers, you simply add or subtract the like terms. Your final answer should be in expression form. For example, when adding

You would add the real number part together and the number part together. In this example, you would add the 2 and 5 together and the 3 and 5 together.

This rule applies to both addition and subtraction. However, multiplying complex numbers is a little bit more tricky.

.: Multiplying Complex Numbers

In order to multiply complex numbers, you must use the distributive property or the FOIL method, just as you do when multiplying real numbers or algebraic expressions.

For example, if you were to multiply

You would first distribute to the rest of the expression

Here is another Example:

Text Box: First use the FOIL method

Next, replace all i2 with -1

Finally, add like terms to get your standard form =

Now that you have mastered multiplying complex numbers, it is time we moved on to something a little bit more difficult. Next I will explain how you can

Plot a complex number on a complex plane.

.: Plotting Complex Numbers

In order to plot a complex number on a complex plane, first you must learn that all real numbers are plotted on the X axis while the imaginary numbers are

Plotted on the Y axis.

For example, if I were to plot -3 + 4i, I would first determine which number was the real number and which was the imaginary. In this example, -3 is the real

Number so it would be plotted on the X axis, while the 4i is the imaginary number, therefore it would only exist on the Y axis. On a plane it would look something

Like this:

Finally, there is one last thing I must teach before I am done. That is the Absolute value of a complex number.

.: Finding the Absolute value of Complex Numbers

“The Absolute value of a complex number z = a+bi, denoted | z |, is a nonnegative real number defined as follows:

Geometrically, the absolute value is its distance from the origin (0,0) and can be solved using the Pythagorean Theorem.

Text Box: The value 8 + 6i is the complex number we are using. A is 8 because it is the real number’s difference from the origin. B is equal to 6 because that is the imaginary number’s distance from the origin. Using the Pythagorean Theorem, if 82 + 62 = |Z|2, 64 + 36 = 100, therefore 100 = |Z|2 or 10 = |Z|. Therefore, the distance 8 + 6i is from the origin is defined as 10.

I am now done, it is now YOUR turn to try your hand at what you have learned today!

.: Practice Problems

1) (17 – i) + (13 + 7i)

2) (14 + 3i) – (4 + 3i)

3) 3i(-7 + 2i)

4) (3 – 5i)(-4 + 2i)

5) Plot 3 + 2i

6) Plot -3i

7) Plot -2 – 3i

8) Find the absolute value of 5 – 4i

9) Find the absolute value of -4 – 3i

10)Find the absolute value of -4i

.: Problem answers (no cheating!)

1) 30 + 6i

2) 10

3) -21i – 6

4) -2 + 26i

5) 6) 7)

8) 6.4

9) 5

10) 4

.: thank you!

This concludes my webpage about Complex Numbers. Incase you were wondering, this entire page was compiled using Microsoft Word, based on a premade template I found.

However, for some reason this template does not let me do what I want it to do, so you can see some of the equations look a little funky. Perhaps that’s just my computer but I

Hope that I can improve on it. Thank you for reading my webpage!!!

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