Complex Natural Logarithm/Examples
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Examples of Complex Natural Logarithm
Logarithm of $-1$
- $\map \ln {-1} = \paren {2 k + 1} \pi i$
for all $k \in \Z$.
Logarithm of $-2$
- $\ln \paren {-2} = \ln 2 + \paren {2 k + 1} \pi i$
for all $k \in \Z$.
Logarithm of $i$
- $\ln \paren i = \paren {4 k + 1} \dfrac {\pi i} 2$
for all $k \in \Z$.
Logarithm of $1 - i \tan \alpha$
- $\ln \paren {1 - i \tan \alpha} = \ln \sec \alpha + i \paren {-\alpha + 2 k \pi}$
for all $k \in \Z$.