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#1 2012-10-10 21:06:41

Deon588
Member
Registered: 2011-05-02
Posts: 68

Principal argument of the polar form of a complex number

Hi all i'm not sure at all how to proceed with this problem, I need to find the principal argument of z but not sure how to go about it...  After googleing I found (theta +2k(pi) =x/r so if I understood correctly (theta +2k(pi) =1/2?
Thanks in advance

View Image: principal argument problem.gif

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#2 2012-10-10 21:31:31

zetafunc.
Guest

Re: Principal argument of the polar form of a complex number

What does |1 + i√3| look like on an Argand diagram?

What is arg(1 + i√3), the angle between (1 + i√3) and the real axis?

#3 2012-10-11 03:52:36

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,092

Re: Principal argument of the polar form of a complex number

hi Deon588

I see you have decided to 'take the plunge!'

When you calculate an inverse sine or cosine your calculator will give one value.  But really, these trig inverse functions are multi-valued.

eg invcos 1/2 = 60 degree ... but also could be 300 degrees or 360 + 60= 420 or 360 + 300 = 660 or ..........

In order to avoid multiple answers your question is just asking for the 'principle' angle, ie 60 degrees or pi/3 if you want it in rads.

(theta +2k(pi) =1/2?

This should be theta + 2k(pi) = invcos(1/2)

By putting k = 1, 2, 3 ... you get all those multiple values.

If you want the principle argument just stop at pi/3 (60)

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#4 2012-10-11 19:54:59

Deon588
Member
Registered: 2011-05-02
Posts: 68

Re: Principal argument of the polar form of a complex number

Thanks Bob your explanation once again makes me able to move forward!!!

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