Results 1 to 3 of 3

Math Help - a + bi form

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    40

    a + bi form

    Put into a + bi form.

    i^102= ?


    i^1802= ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by tmac11522 View Post
    Put into a + bi form.

    i^102= ?


    i^1802= ?
    i^{102} = i^{100} i^2 = (i^{4})^{25} i^2 = \, ....

    Use the same idea with the second one.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    12,110
    Thanks
    976
    i^1 = i
    i^2 = -1
    i^3 = -i
    i^4 = 1

    the pattern repeats as you continue with higher powers of i

    i^{102} = (i^2)^{51} = (-1)^{51} = -1

    or ...

    i^{102} = i^{100} \cdot i^2 = (i^4)^{25} \cdot (-1) = 1^{25} \cdot (-1) = -1

    so ... i^{102} is a real number (imaginary part is zero).


    you try it with i^{1802}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 11th 2010, 12:39 PM
  2. Replies: 1
    Last Post: February 16th 2010, 08:21 AM
  3. Replies: 1
    Last Post: November 27th 2009, 06:33 PM
  4. Replies: 14
    Last Post: May 30th 2008, 07:10 AM
  5. rewrite in slope-intercepr form and general form
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: August 10th 2005, 09:50 PM

Search Tags


/mathhelpforum @mathhelpforum