Complex Numbers - Nomenclature
Maths and statistics discussion, revision, exam and homework help.
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Complex Numbers - NomenclatureOkay, I had a question where I was given a simple complex number in the form a+bi, and asked to put it in polar form. So I changed it to
![\sqrt{a^2+b^2}[cos(\theta )+isin(\theta )], \theta =\frac{b}{a}](http://www.thestudentroom.co.uk/latexrender/pictures/a7/a7eeabffb4d163c0f303c0b567a7b119.png "\sqrt{a^2+b^2}[cos(\theta )+isin(\theta )], \theta =\frac{b}{a}")
. However the answer was in the form of 
. I was under the impression that this was the "Euler form".
Can someone just clear up which form is which so I am not confused from now on ! -
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Re: Complex Numbers - NomenclaturePolar form just means in terms of it's distance from the origin (its 'radius') and its angle from 1. Both of the forms you have given would qualify as some kind of polar form but writing it as an exponent of e is the most common way since it has the same amount of information and is easier to write.
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Re: Complex Numbers - NomenclatureI would always write a complex number in the form
, where r is the modulus of the complex number and 
is another way of saying 
. That's polar form to me.
I almost never use Euler's formula unless I'm proving its validity by the Maclaurin series. -
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Re: Complex Numbers - NomenclatureI would agree that
is much more standard than 
or the quite ugly 
.
However, as usual, if you are answering a question from your course, then what your lecturer/teacher means by 'polar form' will be contained within the content of your course i.e. will have been mentioned in lessons/lectures/the book/lecture notes etc. So the first call would be to reexamine those. I am nearly sure, however, that if you have covered Euler's formula then your teacher/lecturer will either:
a) decree as standard polar form or
b) accept either way of writing it.
