Dividing Imaginary Numbers by Imaginary Numbers

MorPhiend

MorPhiend

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So I was just thinking about imaginary numbers today and their properties. I know. I'm a dork. But I know there are a lot of smart people here and was wondering if someone could explain something to me. I looked all over the web and can only find descriptions of dividing by complex numbers but nothing describing simple imaginary division properties.

Basically, when you take the equation 5i/12i, the answer is 5/12 right? But my understanding is that you can't just cancel out the i's. If you go to WolframAlpha, my suspicion is confirmed as when you click on "Show steps" it shows you have to factor both the numerator and denominator and simplify.

My question is: Why is this? and what would be a good example of where cancelling the i's would give you a wrong answer?

Thanks in advance, this is really bothering me...
 
Its the same thing that will happen when you use the 3DS camera to take a picture of another 3DS's 3D screen. The universe just can't handle the answer.
 
[quote name='RedvsBlue']Its the same thing that will happen when you use the 3DS camera to take a picture of another 3DS's 3D screen. The universe just can't handle the answer.[/QUOTE]

Is the result something like:
129135987821174123.jpg
 
You can cancel out the i's. The computer algorithm sees the denominator in the form A + Bi, which is why you see the factorization.

Here is the wolfram method in a more human readable format:



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Or you can look at like this (might be easier).

sqrt(x)/sqrt(y)=sqrt(x/y)

So, when you take

5i/12i =(5/12)*(i/i)

Substitute i=sqrt(-1)

(5.12)*sqrt(-1)/sqrt(-1)=(5/12)*sqrt(-1/-1)=5/12
 
Oh good! That makes total sense, but I just couldn't find any examples of it (unlike all the examples of multiplying xi by yi) and the funky factoring on WolframAlpha threw me off. Just normal math going on here. Cool, thanks guys! :D
 
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