# Why j for Imaginary Unit?

# Why j for Imaginary Unit?

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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 **i**, **j**, and **k** are used for unit vectors in the directions of the *x*, *y*, 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 **i **and italic *i* point in different directions But bold face **j** and italic *j*both 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.

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Published at DZone with permission of John Cook , DZone MVB. See the original article here.

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