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Math Help - complex numbers

  1. #1
    Junior Member
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    complex numbers

    if z = x+yi prove that:

    abs(e^z)=e^x




    so I can show that e^z = e^x * cisy, I'm not sure what how the absolute value will change this.
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  2. #2
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    Two big hints.
    \left| {cis(t)} \right| = \left| {\cos (t) + i\sin (t)} \right| = \sqrt {\cos ^2 (t) + \sin ^2 (t)}  = ?
    \left| {zw} \right| = \left| z \right|\left| w \right|
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  3. #3
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     e^{z} = e^{x}(\cos y + i \sin y) . Thus  |e^{z}| = |e^{x}| \cdot |\cos y + i \sin y| = e^{x} . As Plato hinted, the modulus of the second term is  1 .
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