Jump to content

Complex numbers - polar form?


Melissi

Recommended Posts

Hi again!

I'm (still) doing complex numbers revision and while that isn't going too badly altogether, I noticed something in the answers to the calculations in polar form: sometimes (seemingly for no reason) 2pi has been subtracted from the argument, whereas sometimes it hasn't been. This seems like a really small and insignificant question, but if complex numbers is one of the topics I can do reasonably well, then I don't want to lose marks on little things like this, so my question is: is there any particular reason why 2pi is subtracted only sometimes? There really isn't anything that I can see to tell the difference between questions!

Thank you! :)

Link to post
Share on other sites

Do keep in mind both sin(x) and cos(x) are cyclic mod 2pi, hence cis(x) and e^(i*x) are as well. So I would assume they subtract or add 2pi to the argument in order to keep the argument within a certain domain - I'm not sure if this is [0,2pi) or (-pi,pi]. That's my best guess!

  • Like 3
Link to post
Share on other sites

Thanks! I did think of that, but the questions (1c and 2a in this picture, though there were others as well) don't give a range for the values to be in, which is why I was a bit confused.

I suppose it's likely that they were keeping the answers within a range that just wasn't specified, though that's a bit annoying. Thank you anyway :)

post-133137-0-20666000-1393685779_thumb.

Link to post
Share on other sites

Oh for this, because the Value of Cos and Sin are cyclic, they will repeat after every 2pi, so you add 2(k)pi to pi/5 where k = 0,1,2,3,4,5,
and then you use the De-Moivers Theorem like normal. I think that should do it if I'm not wrong

P.S - I was in the same position as you, I'm pretty sure about my answer but am kinda unsure as to how many values of k are necessary.

  • Like 1
Link to post
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...