Why j for Imaginary Unit?

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.