Results 1 to 2 of 2

Math Help - Complex Numbers

  1. #1
    Member classicstrings's Avatar
    Joined
    Mar 2006
    Posts
    175
    Awards
    1

    Complex Numbers

    Stuck on a few....

    I think this has something to do with the following questions:

    sin(theta) + cos(theta)i = cis(pie/2 - (theta))

    Simplify

    a. (cos(theta)-sin(theta)i)^5

    b. (sin(theta) + cos(theta)i)(cos(theta) + sin(theta)i)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,888
    Thanks
    326
    Awards
    1
    Quote Originally Posted by classicstrings View Post
    Stuck on a few....

    I think this has something to do with the following questions:

    sin(theta) + cos(theta)i = cis(pie/2 - (theta))

    Simplify

    a. (cos(theta)-sin(theta)i)^5

    b. (sin(theta) + cos(theta)i)(cos(theta) + sin(theta)i)
    a)  [cos(\theta) - i \cdot sin(\theta)]^5 = cos(5 \theta) - i \cdot sin(5 \theta)
    (Similar to [cos(\theta) + i \cdot sin(\theta)]^n = cos(n \theta) + i \cdot sin(n \theta))

    b) Just expand:
    [sin(\theta) + i \cdot cos(\theta)][cos(\theta) + i \cdot sin(\theta)]

     = [sin(\theta) cos(\theta) - sin(\theta) cos(\theta)] + i \cdot [sin^2(\theta) + cos^2(\theta)] = i

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. raising complex numbers to complex exponents?
    Posted in the Advanced Math Topics Forum
    Replies: 10
    Last Post: March 25th 2011, 10:02 PM
  2. Replies: 1
    Last Post: September 27th 2010, 03:14 PM
  3. Replies: 2
    Last Post: February 7th 2009, 06:12 PM
  4. Replies: 1
    Last Post: May 24th 2007, 03:49 AM
  5. Complex Numbers- Imaginary numbers
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 24th 2007, 12:34 AM

Search Tags


/mathhelpforum @mathhelpforum