Tuesday, March 24, 2015

Imaginary Numbers Revisited

I am guessing I know what you are thinking:  Imaginary Numbers are something as useful in the real world as the stories of Alice in Wonderland (or, more accurately, “Alice’s Adventures in Wonderland”).

Although most of us seldom or ever run into any reference to Imaginary Numbers, there is a small faction of individuals in the sciences, such as electrical engineering, that could not succeed well without them.  The analysis of AC circuits, for example, would not be possible without these oddities in the math world.

If you are involved in an academic Math Curriculum (student or instructor), however, you will almost certainly encounter and use Imaginary Numbers at some time during your studies.

For those of us who have not had a math class in a long while, (or if you are not a Math Geek like me), a brief review of Imaginary Numbers is in order. They are simply a number that can be written as a real number multiplied by the Imaginary Unit i. The Square of i is -1. An imaginary number has a negative or zero square. For example, 5i is an imaginary number, and its square is -25.

In terms of imaginary numbers, the Square Root of -9 is 3i.

They are nothing at all new, as they were conceived in ancient Greece by a brilliant mathematician and engineer by the name of Hero of Alexandria. “Hero” (that’s quite a name, isn’t it?...) is noted for many inventions, including the first-recorded steam engine and a rocket-like reaction engine.  Not bad a first-century Greek.

So, what about Excel?  Interestingly, Excel can easily handle these oddities of the math world. It even has a couple of specially designed functions to deal with Imaginary and Complex (expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, where i2 = −1).

The Imaginary function operates with the syntax:

The Complex function uses this syntax:
   =COMPLEX(realnumber, inumber, [syntax])

There are also several built-in tools in Excel for using imaginary numbers with typical arithmetic functions of addition, multiplication, etc.

So, why am I even discussing this topic today?  Well, if you have children in school, I wouldn’t be surprised if your son or daughter comes home one day with homework involving Imaginary Numbers.  Wouldn’t it be cool if you could show them how this can be done in Excel?  It may even be a surprise for her or his teacher! 

Imaginary Numbers.  Not just topics for Alice and the White Rabbit...

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