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: Expanding Euler's Identity

  1. Aug 5, 2015 #1
    1. The problem statement, all variables and given/known data

    ## y^({9}) + y''' = 6 ##

    2. Relevant equations


    3. The attempt at a solution

    ## y^({9}) + y''' = 6 ##

    ## r^9 + r^3 = r^{3}(r^{6}+1)=0 ##

    ## r = 0, m = 3 ##

    ## r^6 + 1 = 0 = e^{(i(\pi + 2k\pi)} ##

    ## r = -1 = e^{i(\frac {\pi +2k\pi} {6})} ##

    ## k = 0 , r = e^{i(\frac {\pi} {6})} ##

    ## k = 1 , r = e^{i(\frac {\pi} {2})} ##

    ## k = 2 , r = e^{i(\frac {5\pi} {6})} ##

    My question is, when doing the ##k = 0,1,2, ... ## How does the ##e^{i\pi}## expand? My teacher has the answer for ## k = 0 ## as:

    ## r = e^{i(\frac {\pi} {6})} = \frac {\sqrt{3}} {2} + \frac {i} {2}##

    I don't understand how the exponential works out to the ##\frac {\sqrt{3}} {2} + \frac {i} {2}##
     
  2. jcsd
  3. Aug 5, 2015 #2

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Remember, eix = cos (x) + i sin (x). If x = π/6, then eix = ?

    https://en.wikipedia.org/wiki/Euler's_identity
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Loading...