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\(log(e^{1+2i})\)

Here i mean log base 10 not base e

 Aug 17, 2016
 #1
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(1+2 i)/(log(10))

=0.43429448190325182765112891891660508229439700580366656611... +
0.86858896380650365530225783783321016458879401160733313222... i

 Aug 17, 2016
 #2
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This looks hard but I will give it a try.

\(\text{Let }x=\log\left(e^{(1+2i)}\right)\\ 10^x= e^{1+2i}\\ 10^x=e\times (e^i)^2\)

 

 

\(e^{i\pi}+1=0\\ (e^i)^\pi + 1=0\\ (e^i)^\pi=-1\\ e^i=(-1)^{\frac{1}{\pi}}\)

 

\(10^x=e\times (-1)^{\frac{2}{\pi}}\\ 10^x = e\times (1)^{\frac{1}{\pi}}\\ 10^x = e\\ x = \log e\)

 Aug 17, 2016

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