1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Complex Analysis Properties Question 2

  1. Jun 16, 2015 #1


    User Avatar
    Gold Member

    The problem states, Show that:
    a) |e^(i*theta)| = 1.
    Now, the definition of e^(i*theta) makes this
    If we choose any theta then this should be equal to 1.

    What can help me prove this? If I choose, say, pi/6 then it simplifies to |(sqrt(3))/2+i/2)| which doesn't seem to equal 1.

    b) BAR(e^(i*theta)) = e^(-i*theta)

    Here's what I think. The bar e^(i*theta) means that the definition is cos(theta)-isin(theta) and this can be rewritten as cos(-theta)+i*sin(-theta) which can be inputted back into the definition to see that e^(-i*theta) is correct.
  2. jcsd
  3. Jun 16, 2015 #2


    User Avatar
    Science Advisor
    Homework Helper

    Uh, ##|x+iy|=\sqrt{x^2+y^2}##, yes? So?
  4. Jun 16, 2015 #3


    User Avatar
    Gold Member

    Ok, so when we have |cos(theta)+isin(theta)| this can be represented as sqrt(cos^2(theta)+sin^2(theta)) and this is clearly equal to 1, always.

    Ah, that is simply beautiful.
    I appreciate your guidance here. Swiftly helped me here.
  5. Jun 20, 2015 #4
    It does.
  6. Jun 20, 2015 #5


    User Avatar
    Science Advisor
    Gold Member

    Also, I am not sure what the starting point is, what you can assume, but ## cos\theta+ isin\theta ## is a parametrization for a point in the unit circle.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Complex Analysis Properties Date
Prove that this function is holomorphic Friday at 11:45 PM
Cauchy Integration Formula Jan 13, 2018
Laurent series of z^2sin(1/(z-1)) Jan 11, 2018
Complex Analysis Properties Question Jun 16, 2015
Complex Analysis: Properties of Line Integrals Oct 12, 2011