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My lecturer stated that the principal argument is $[0,2\pi)$. However my tutor (my tutor is different to my lecturer) states that it is $(-\pi, \pi]$. Wikipedia article on complex numbers mentions both of these. In my test I used $[0,2\pi)$ convention and not the other one so my tutor deducted 0.5 mark. So which one is correct? and is it fair that I loose 0.5 mark here?

Is there any difference between principal argument and principal argument in the exponential polar form?

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Both are correct, just keep track of who is asking. There are many places in mathematics where more than one convention is used, sometimes according to country, all sorts of things. –  Will Jagy Oct 22 '12 at 3:29
    
I'd say both are wrong if they were so careless as to categorically claim that this or that value is "the principal" one. –  DonAntonio Oct 22 '12 at 3:56

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