# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Wed, 19 Jun 2013 01:47:43 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 6 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: De Moivre question (complex numbers)Posted: Sat, 23 Oct 2010 15:05:28 UTC
 Senior Member

Joined: Mon, 19 Apr 2010 13:45:05 UTC
Posts: 61
De Moivre's Theorem says that if is real, then for all n E Z.

By considering real parts, find an expression for in terms of powers of and .

Attempt:

but this wasnt the correct answer.

Top

 Post subject: Re: De Moivre question (complex numbers)Posted: Sat, 23 Oct 2010 15:17:13 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6066
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
TsAmE wrote:
De Moivre's Theorem says that if is real, then for all n E Z.

By considering real parts, find an expression for in terms of powers of and .

Attempt:

but this wasnt the correct answer.

_________________

Top

 Post subject: Posted: Sun, 24 Oct 2010 01:29:44 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 10 Jan 2007 19:16:15 UTC
Posts: 652
Location: England
Okay, I want to have a stab at this one:

Now we want the real parts, which is everything without an i in it. So

Then, ofc, as you could write it as a sum of cosines, but if your answer is in sines and cosines then the above should be fine

_________________
"It's never crowded along the extra mile"

Graduated, and done with maths forever

Top

 Post subject: Posted: Sun, 24 Oct 2010 13:47:50 UTC
 Senior Member

Joined: Mon, 19 Apr 2010 13:45:05 UTC
Posts: 61
Thanks a lot. For the last question it asked write in terms of powers of .

In this case how would this be possible since is imaginary?

Top

 Post subject: Posted: Sun, 24 Oct 2010 14:24:55 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Wed, 10 Jan 2007 19:16:15 UTC
Posts: 652
Location: England
For take all of the imaginary terms in the expansion of . Then use to rewrite the terms with cosines in them

_________________
"It's never crowded along the extra mile"

Graduated, and done with maths forever

Top

 Post subject: Posted: Sun, 24 Oct 2010 15:55:38 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12167
Location: Austin, TX
TsAmE wrote:
Thanks a lot. For the last question it asked write in terms of powers of .

In this case how would this be possible since is imaginary?

It's not imaginary, it's the imaginary part of the complex number. If you don't get it you should remember that x+iy is complex, but the point is that y itself is real.

_________________
(\ /)
(O.o)
(> <)
This is Bunny. Copy Bunny into your signature to help him on his way to world domination

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 6 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous