Difference between revisions of "Real and imaginary parts of log"

From specialfunctionswiki
Jump to: navigation, search
 
Line 7: Line 7:
  
 
==References==
 
==References==
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm|next=Polar coordinates}}: 4.1.2
+
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Logarithm|next=Polar coordinates}}: $4.1.2$
  
 
[[Category:Theorem]]
 
[[Category:Theorem]]
 
[[Category:Unproven]]
 
[[Category:Unproven]]

Latest revision as of 17:23, 27 June 2016

Theorem

Write $z \in \mathbb{C}$ using polar coordinates: $z=x+iy=re^{i\theta}$. The following formula holds for $-\pi < \mathrm{arg}(z) \leq \pi$: $$\log(z)=\log(r)+i\theta,$$ where $\mathrm{arg}$ denotes the argument and $\log$ denotes the logarithm.

Proof

References