- #1

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## Homework Statement

I want to show that

[tex] \exp \left( i\bar{z} \right) = \overline{\exp \left( iz \right)} [/tex]

if and only if

[tex] z = n\pi [/tex]

for any integer n.

## Homework Equations

## The Attempt at a Solution

Utilizing Euler's formula, I got

[tex] \cos \bar{z} = \cos z [/tex]

and

[tex] \sin \bar{z} = -\sin z [/tex]

Though not fully convinced, I concluded that

[tex] \bar{z} = z [/tex]

This then led me to

[tex] \sin z = 0 [/tex]

This obviously led me to the needed conclusion. But was I correct?