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Question Number 197184 by pete last updated on 10/Sep/23

Show that \log (- \log i) = \log (\frac{π}{2}) - i \frac{π}{2}

Answered by Frix last updated on 10/Sep/23

\ln (- \ln i) = \ln \frac{π}{2} - i \frac{π}{2}

- \ln i = e^{\ln \frac{π}{2} - i \frac{π}{2}}

- \ln i = \frac{π}{2} e^{- i \frac{π}{2}}

- \ln i = - \frac{π}{2} i

\ln i = \frac{π}{2} i

i = e^{i \frac{π}{2}}

i = i true

Commented by pete last updated on 10/Sep/23

Thank you sir

Commented by Frix last updated on 10/Sep/23

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