Question 1061463
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*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 7.66\ =\ 5.4(1\ +\ i)^6]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ (1\ +\ i)^6\ =\ \frac{7.66}{5.4}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log\left((1\ +\ i)^6\right)\ =\ \log\left(\frac{7.66}{5.4}\right)]


Note: Using base 10 logarithms but any base can be used.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 6\,\cdot\,\log(1\ +\ i)\ =\ \log\left(\frac{7.66}{5.4}\right)]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \log(1\ +\ i)\ =\ \frac{\log\left(\frac{7.66}{5.4}\right)}{6}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\ +\ i\ =\ 10^{\frac{\log\left(\frac{7.66}{5.4}\right)}{6}}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ i\ =\ 10^{\frac{\log\left(\frac{7.66}{5.4}\right)}{6}}\ -\ 1]


The rest is just calculator work


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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