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Math Help - complex number exponential form

  1. #1
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    complex number exponential form

    Hi

    Can someone please help me on the following question

    Write w=e^1+3i in Cartesian form.

    thanks
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  2. #2
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    e^{x + yi}  = \left[ {e^x \cos (y)} \right] + i\left[ {e^x \sin (y)} \right]
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    thats in polar form though. How would you get it into catesian ?
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    Quote Originally Posted by rpatel View Post
    thats in polar form though. How would you get it into catesian ?
    I really don't understand your confusion.
    The following is produced by the CAS MathCad.
    Attached Thumbnails Attached Thumbnails complex number exponential form-cart.gif  
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  5. #5
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    Quote Originally Posted by rpatel View Post
    thats in polar form though. How would you get it into catesian ?
    It's not because there are exponentials that it is still in polar form.

    In cartesian form, it would be like a+ib, where a and b are real numbers.

    But e^x is a real number, for any real x.
    So e^x \cos(y) is real and e^x \sin(y) is real.

    The formula Plato gave is, without any doubt, a cartesian form, the one corresponding to e^{x+iy}.
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