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#1 2012-10-11 20:06:41
- Deon588
- Full Member
Offline
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
#2 2012-10-11 20:31:31
- 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 2012-10-12 02:52:36
- bob bundy
- Moderator
Online
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