Results 1 to 3 of 3

Math Help - Product of Complex Numbers proof

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    86

    Product of Complex Numbers proof

    If x1 + iy1 is an element of C and has an absolute value r1 and argument phi1, and

    x2 + iy2 is an element of C and has absolute value r2 and argument phi2, then

    the product (x1 + iy1)(x2 + iy2) has absolute value r1r2 and argument (one among many) phi1 + phi2


    where C is the set of complex numbers. Any help would be appreciated for this proof!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    29
    First thing to do is expand (x_1 + iy_1)(x_2 + iy_2) , then re-write the result as x+yi and find r and \phi
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2010
    Posts
    715
    Thanks
    2
    (x_1 + iy_1)(x_2 + iy_2) = r_{1}e^{i\varphi_{1}}r_{2}e^{i\varphi_{2}} = r_{1}r_{2}e^{i(\varphi_{1}+\varphi_{2}).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Product of complex numbers in polar form
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: July 19th 2011, 09:03 AM
  2. complex numbers - product of polar forms
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: April 10th 2011, 02:13 PM
  3. Product of complex numbers.
    Posted in the Algebra Forum
    Replies: 4
    Last Post: September 12th 2010, 11:09 AM
  4. find the product and its conjugate-complex numbers
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: August 11th 2009, 11:37 AM
  5. Product of n numbers = 1, sum >= n - Proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: July 7th 2009, 12:20 PM

Search Tags


/mathhelpforum @mathhelpforum