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Algebra Level pending

$\Re[ \; \ln (1+i) \; ]$

Calculate the real part of the complex number $\ln (1+i )$ correct to three decimal places.

1 solution

Jason Simmons
Dec 28, 2015

$\textrm{Log} (z) = \ln |z| +i \textrm{Arg} (z), \: z \in \mathbb{C}$

$\textrm{Log} (1+i) = \ln |1+i| +i \textrm{Arg} (1+i)$

$\textrm{Log} (1+i) = \ln \sqrt{2} + \frac{i \pi}{4} \: \: \Rightarrow \: \: \ln (1+i) = \ln \sqrt{2} +\frac{i \pi}{4}$

$\Re [ \; \textrm{Log} (1+i) \; ] = \ln \sqrt{2} \approx \boxed{0.347}$