# Use of i and j in complex numbers

• chwala
In summary: So, I guess my main point is that there's nothing really wrong with the convention ##j##, as long as everyone is using the same notation. Personally I like to use ##i##, but that's just me.In summary, there is no specific reason as to why certain texts use ##j## and others ##i## when looking at complex numbers. Maths is a relatively easy subject but at times made difficult with all this mix-up... i tend to use a lot of my time in trying to understand author's language and this is also evident on the convention used on argument, an area that is pretty easy/straightforward to me...this is akin to the mix up/confusion on the standard
chwala
Gold Member
Homework Statement
See attached
Relevant Equations
complex numbers
Is there any particular reason as to why certain texts use ##j## and others ##i## when looking at complex numbers? Maths is a relatively easy subject but at times made difficult with all this mix-up... i tend to use a lot of my time in trying to understand author's language and this is also evident on the convention used on argument, an area that is pretty easy/straightforward to me...this is akin to the mix up/confusion on the standard way of expressing derivatives noting that the two great mathematicians :Sir Isaac Newton and Leibnitz had different notations...

anyway, which is the standard way of expressing complex numbers?

Last edited:
Electrical engineers tend to use j so it is not confused the current in a circuit.

PhDeezNutz, Steve4Physics, berkeman and 2 others
chwala said:
Homework Statement: See attached
Relevant Equations: complex numbers

Is there any particluar reason as to why certain texts use j and others i when looking at complex numbers?
It's a pretty meaningless convention IMO. Why are is e used as the base of natural logarithms, π the ratio of diameter to circumference?

I will say EEs like to use ##j## since we use ##i## for current. OTOH physicists use ##j## for current density. But it wouldn't have to be that way.

chwala
DaveE said:
It's a pretty meaningless convention IMO. Why are is e used as the base of natural logarithms, π the ratio of diameter to circumference?

I will say EEs like to use ##j## since we use ##i## for current. OTOH physicists use ##j## for current density. But it wouldn't have to be that way.
Agreed, but at times the convention may in away create some mix-up. On a pretty straightforward concept. Like this for example,

chwala said:
Agreed, but at times the convention may in away create some mix-up. On a pretty straightforward concept. Like this for example,

View attachment 329352
OK, LOL. That isn't confusing to me, but that's just because I'm used to seeing it. BTW, I never really liked that "angle" symbol (∠). To me that's ##2e^{-j\frac{\pi}{6}}##. So personal preference is sometimes at play too.

One thing you will find as you continue in the physical sciences is that different people write stuff with different conventions; what they like, or how they learned things. It can be quite annoying at times, but part of the work is translating nomenclature. Context is key in deciphering this stuff.

As an aside, I'd like to shout out Born & Wolf "Principles of Optics", a text that everyone says is a classic, but I found nearly unreadable because they never used the same variable names I was taught. I hated that book simply for these reasons. You'll figure out your own favorite way and your own favorite texts, I'm sure. If you are too weird in your definitions, you'll have a hard time explaining stuff to others.

I guess I'm pretty amazed at how much standardization there is.

hutchphd and chwala
chwala said:
Agreed, but at times the convention may in away create some mix-up. On a pretty straightforward concept. Like this for example,

View attachment 329352
That's called Steinmetz notation (after the electrical engineer Steinmetz, by many considered the father of modern electrical engineering) and it is just the polar form of a complex number. It's quite ingenious, for one only needs the angles in electric circuit algebra. Well, Steinmetz was indeed a genius.

Inventing or using clever notation is a huge help in creative thinking. All great scientists introduced notations of their own in their work. Take, for instance, Einstein's notation of partial derivatives with commas; or better index notation in linear algebra. Or Feynman's, which perhaps are too many to mention. (One of his first novel notations was with trigonometric functions in his junior high school years.)

As a matter of fact, Feynman used to emphasize the usefulness of good notation. He also talked about that in his Lectures on Physics (for instance, Vol. I, Chapter 17, Section 17-5; read the passage---you will find it quite illuminating).

chwala

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