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Loser66
 one year ago
If \(z \in \mathbb C\), verify
\(\overline {e^z}= e^{\overline {z}}\)
Please, help
Loser66
 one year ago
If \(z \in \mathbb C\), verify \(\overline {e^z}= e^{\overline {z}}\) Please, help

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1try using the series definition of e^z

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0\(e^z = \sum_{n=0}^\infty \dfrac{z^n}{n!}\) right?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2hint: \[\Large \overline {{e^z}} = \overline {{e^{x + iy}}} = \overline {{e^x}{e^i}^y} = {e^x}{e^{  i}}^y = ...?\]

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0oh, yeh!! because e^x is a real part, hence it doesn't change under the"bar" , right?

Loser66
 one year ago
Best ResponseYou've already chosen the best response.0ha!! one line proof!!!

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! furthermore we have the subsequent theorem: \[\Large \overline {{z_1}{z_2}} = \overline {{z_1}} \;\overline {{z_2}} \]
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