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Math Help - Domain and Range of Complex Functions

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    Domain and Range of Complex Functions

    Determine the domain and range of the complex function:
    f(z)=e^{(x-y)\mathbf{i}}

    I know that forum wish that questions have worked associated with what one needs help with; however, my book doesn't help whatsoever in finding the domain and range. Therefore, I can't supply any work since I have no idea how do this problem. Can someone help me with solving this problem, thanks.
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    The function

    e^{i\theta} for real theta is always on the unit circle. So in your case you have \theta=x-y So x and y can take on any values but the the immage will always lie on the unit circle in \mathbb{C}
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    The domain then is \mathbb{C} and the range is simple the unit circle.
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    How can I determine a number w such that w isn't in the range?
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