1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Problem regarding complex numbers

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data

    If m and x are two real numbers where m ε Integers, then e2micot-1x{(xi+1)/(xi-1)}m, (where i=√(-1)) is equal to :

    (a) cos(x) + isin(x)
    (b) m/2
    (c) 1
    (d) (m+1)/2

    2. Relevant equations

    3. The attempt at a solution

    I seriously have no clear cut idea of how to proceed. I used this technique,

    Since m is an integer, then I put m=0, and got the correct answer. :p

    But I want a procedure, not a hit and trial method, of how to proceed.

    I can write above as

    {cos (2mcot-1x) + isin(2mcot-1x)}{(xi+1)/(xi-1)}m

    But how to proceed after this ? Hints will do..

    Please help !!

    Thanks in advance...:smile:
  2. jcsd
  3. Dec 13, 2013 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    First of all: what is meant by ##\cot^{-1} x?## (I know it, but do you?) Try to set ##y = \cot^{-1} x## and see where that gets you.
  4. Dec 13, 2013 #3
    Hello sankalp!

    Look at ##xi+1##. Can you convert it to e^{i*something}? :)
  5. Dec 13, 2013 #4
    I know what it is. Its an inverse trigonometric function with range 0 to pi, boundaries exclusive. Are you insisting to substitute y with cot inverse x ?
    Yeah. I got the answer. Thanks.

    Rays approach also worked.


    The question you asked in one post was from present fiitjee aits. Are you giving a second try for jee ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted