Complex Natural Logarithm/Examples

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 $k \in \Z$.