Complex Numbers are imaginary numbers. Before reading this post, you might want to watch Barney to get that old dusty thing people call "imagination" or what muggers call "a useless waste of brain power" fired up. Ready? How's it running? What with all the mugging, I bet it's not been turned on for a while, yeah? They could have at least warned us this was coming. Most of us lost our imagining skills 1 year and 8 months ago. Or 8 months for some. Anyway, down to business.
This is a crash course on imaginary numbers. As I have mentioned, Complex Numbers are imaginary numbers. You have to imagine them. This requires your imagination. Say it with me. EE-MAGH-EE-NAY-SHUN. Good! Now, imagining stuff is ok for kids, but after you age till about...say 17, you start to lose it the more you study. Which is why Complex Numbers are tested.
Now look at the number below. Remember to quickly look back before your brain explodes! Ready? Go! How was it? Scary? Looks vulgar and unnatural right? Do you feel that a fundamental law of reality was just been broken? Does it look like it shouldn't exist? There's a primal sense of the laws of nature being violated. Felt like you were falling into an endless pit through a rift in reality? Don't worry. All you need is IMAGINATION! Tell yourself, I can root a negative number. I can root a negative number. Its ok, I won't get hurt. Look at the number. Remember to stop if you feel any headaches. With practice, you won't get that MY-BRAIN-IS-IMPLODING feeling anymore.
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(I'm using my main com to bring you this, so I can't get the same control as on my laptop, so its a tad ugly.) Now look at the picture below. the "a" part is real, dont worry, but the "bi" part is not. Or "b" part.You should see the text "a+bi" both on top and at the bottom of the picture. It takes imagination!
So if you see "a+b" ONLY, it means your imagination isn't strong enough to produce an i on the screen. If you see only one "i", it means your imagination can only handle one imaginary number at one time. You need to train it up more. Try focusing all your energy on the blank spot where the "i" is. Stare at it for a few seconds. It might slowly appear if you try hard enough. If it fades in and out, you're almost there, just practice a little more.
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Our advice is to watch Barney. If you think its ridiculous, we think so too! The show, that is. However, it takes real practice and skill to imagine a big fat human-sized purple and green dinosaur with no genitalia whatsoever clomping about onscreen for 30 minutes! But if a 3 year old can do it, so can you!
It's best to train up your imagination early, or else you'll go into the exam hall and screw up all your complex numbers questions. Imagine seeing (5+3i)^2 as (5+3)^2! Next week, we shall be discussing how complex numbers actually caused the creation of the Bermuda Triangle, figure in the evolution of Bigfoot, and find out the link between Santa Claus, the Tooth Fairy, Perfect Competition, and complex numbers.
