Loser66
  • Loser66
If \(z \in \mathbb C\), verify \(\overline {e^z}= e^{\overline {z}}\) Please, help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ganeshie8
  • ganeshie8
try using the series definition of e^z
Loser66
  • Loser66
\(e^z = \sum_{n=0}^\infty \dfrac{z^n}{n!}\) right?
Michele_Laino
  • Michele_Laino
hint: \[\Large \overline {{e^z}} = \overline {{e^{x + iy}}} = \overline {{e^x}{e^i}^y} = {e^x}{e^{ - i}}^y = ...?\]

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Loser66
  • Loser66
oh, yeh!! because e^x is a real part, hence it doesn't change under the"bar" , right?
Loser66
  • Loser66
ha!! one line proof!!!
Michele_Laino
  • Michele_Laino
yes! furthermore we have the subsequent theorem: \[\Large \overline {{z_1}{z_2}} = \overline {{z_1}} \;\overline {{z_2}} \]
Loser66
  • Loser66
Thanks so much.

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