Results 1 to 4 of 4

Math Help - Complex numbers, don't understand last bit! :(

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    15

    Unhappy Complex numbers, don't understand last bit! :(

    Hey guys i was working through this question and when i cheked my answers i realised there was an extra bit to do to get the final answer but i dont know wt im supposed to do:

    Q) Express (-1 + sqrt3i) in modulus-argument form. Evaluate (-1 + sqrt3i)^8,
    expressing your answer in a + ib form.

    I got z= 2cis 2pi/ 3 for mod -arg form but when i evaluate it I can get to:

    2^8 cis 16pi/3

    but then the answers tell me tht the answer above is equal to 2^8 cis 4pi/3???

    And that the final answer in a+ ib form is : -128 - 128sqrt3i .

    What i want to know is how do i go from 2^8 cis 16pi/3 ==> -128 - 128 sqrt3i??
    Last edited by Latkan; May 3rd 2010 at 05:48 AM. Reason: missed out a part of my answer
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    You need to realize that \frac{16\pi}{3}=4\pi+\color{blue}\frac{4\pi}{3}.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2009
    Posts
    15
    i figured that was the case but how am i supposed to work that out for something like:

    2^10 cis 40pi/3

    is there a certain method etc?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Aug 2009
    From
    Israel
    Posts
    976
    \frac{40 \pi}{3} = \frac{ (6 \cdot 3) \cdot 2 \pi + 4 \pi}{3} = 12 \pi + \frac{4 \pi }{3}

    Simply find out the largest multiple of 2 \pi times the denominator, and "subtract" it from the numerator - in this example, 6 * 3, and in your previous example, 2*3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A set of numbers which i dont understand.
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: June 30th 2011, 10:32 AM
  2. Replies: 2
    Last Post: May 28th 2011, 02:34 PM
  3. Replies: 1
    Last Post: September 27th 2010, 03:14 PM
  4. Replies: 7
    Last Post: October 3rd 2009, 03:43 AM
  5. Replies: 1
    Last Post: May 24th 2007, 03:49 AM

Search Tags


/mathhelpforum @mathhelpforum