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John Cook is an applied mathematician working in Houston, Texas. His career has been a blend of research, software development, consulting, and management. John is a DZone MVB and is not an employee of DZone and has posted 172 posts at DZone. You can read more from them at their website. View Full User Profile

Why j for Imaginary Unit?

04.23.2013
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Electrical engineers use j for the square root of -1 while nearly everyone else uses i. The usual explanation is that EE’s do this because they use i for current. But here’s one advantage to using j that has nothing to do with electrical engineering.

The symbols ij, and k are used for unit vectors in the directions of the xy, and z axes respectively. That means that “i” has two different meanings in the real plane, depending on whether you think of it as the vector space spanned by i and j or as complex numbers. But if you use j to represent the imaginary unit, its meaning does not change. Either way it points along the y axis.

Said another way, bold face and italic i point in different directions But bold face j and italic jboth point in the same direction.

Here’s what moving from vectors to complex numbers looks like in math notation:

And here’s what it looks like in electrical engineering notation:

I don’t expect math notation to change, nor would I want it to. I’m happy with i. But using j might make moving between vectors and complex numbers a little easier.

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By the way, I use j on @DSP_fact. DSP came out of electrical engineering, so j is conventional there. I also use j in Python because that’s what the language requires.

Published at DZone with permission of John Cook, author and DZone MVB. (source)

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