Formula:1675

Digital Library of Mathematical Functions ID 4.8.E6

${\displaystyle{\displaystyle\ln\left(z^{n}\right)=n\ln z,}}$

Constraint(s)

${\displaystyle{\displaystyle n\in\mathbb{Z}}}$
${\displaystyle{\displaystyle-\pi\leq n\operatorname{ph}z\leq\pi}}$

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathbb{Z}}}$:
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle n}}$: integer
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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