Introduction to complex numbers (HW1, ECE301, Fall 2008)
A complex number consists two parts?: a real part and an imaginary part. Here is an example:
$ 35 + j12\! $
In the example, the real part of the number of $ 35 $ and the imaginary part is $ 12 $. Note that the letter $ j $ is not included in the imaginary part. It, instead, is a marker, used to identify which part of the complex number if imaginary. Also, note that the imaginary part is usually marked with an $ i $. However, since $ i $ is used to symbolize current in electrical applications, most electrical engineers, computer engineers, computer scientists, and physicists specializing in electrical fields use $ j $ and a substitute for the indicator of the imaginary part of a complex number.
Determining magnitude
So how do we determine the magnitude of a complex number? Well, my friend, the answer is really quite simple. Take the aforementioned example:
$ 35 + j12\! $
We can imagine (get the pun?) this number as a set a coordinates on a two-dimensional plane, much like the xy-plot. The x-coordinate is replaced with the real part of our complex number, in this case $ 35 $. The y-coordinate is replaced with the imaginary part, which is $ 12 $ in this case. Thus, we have a plot, on which the horizontal axis is real, and the vertical axis is imaginary.
The magnitude of an imaginary number is defined as the distance between the plotted point of the number of such a two-dimensional plane and the origin, which is $ 0 + j0 $. This can be computed easily with the equation:
$ Mag = \sqrt((Re)^2 + (Im)^2)\! $
Where $ Mag $ is the magnitude, $ Re $ is the real part, and $ Im $ is the imaginary part. Therefore, the magnitude of the example is as follows:
$ Mag = \sqrt((35)^2 + (12)^2)\! $
Which would give you the value $ 37 $, according to Google's reliable calculator.
I hope you have enjoyed reading about how to find the magnitude of imaginary numbers. If this is not clear, I am very sorry, but I am an electrical engineering major at Purdue. I don't have that much time. Right now, it is midnight, so I bid you adieu.
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