Results 1 to 2 of 2

Math Help - Complex number

  1. #1
    Junior Member
    Joined
    Aug 2009
    Posts
    62

    Complex number

    Hi everybody,

    How to show that: \forall a \in \mathbb{C}*, \exists z_0 \in \mathbb{C} such as: a=e^{z_0}, and if e^z=a then \exists k \in \mathbb{Z}: z=z_0+2k\pi, i don't know how to show that, can you help me please???

    And thanks anyway.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie driegert's Avatar
    Joined
    Feb 2010
    From
    Kingston, Ontario
    Posts
    16
    Hey there.

    So just as a reminder we know that you can represent a complex number z as:

    z = x + iy in rectangular coordinates or
    z = re^{i \theta} where  r = \sqrt{x^{2} + y^{2}} and \theta = tan^{-1}(y/x) in polar coordinates (you have to adjust theta for the quadrant depending on the signs on x and y).

    Anyways,

    e^{z} = e^{x + iy} = e^{x}e^{iy} By Euler's formula we can change the second e like this:

    e^{x}e^{iy} = e^{x}(cos(y) + isin(y))

    So actually, now that I've done that.. it's not going to work out at all unless you actually meant:

     z = z_{0} + 2ik \pi

    So you need an 'i' term with the 2k \pi term.

    So yeah... If there wasn't a typo, perhaps some of my rambling will jog your memory.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 2nd 2010, 01:54 PM
  2. Replies: 3
    Last Post: September 13th 2010, 11:13 AM
  3. Sin of Complex Number
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 31st 2009, 05:40 PM
  4. Complex number
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: August 14th 2009, 05:56 AM
  5. Complex number help??
    Posted in the Algebra Forum
    Replies: 4
    Last Post: March 22nd 2008, 02:23 AM

Search Tags


/mathhelpforum @mathhelpforum