# Get argument formula of a complex number with integer variable?

Posted 1 year ago
1056 Views
|
3 Replies
|
2 Total Likes
|
 Hello everyone. I have the complex number (1 - E^2) (2 + I 2 Pi k) with k integer. How can I get the general formula for the argument? It should be Pi+ArcTan[k Pi] if k>0.I tried with: Assumptions->Element[k,Integers] Assumptions -> k > 0 Arg[(1 - E^2) (2 I Pi k)] but it does not work.Thank you very much.
3 Replies
Sort By:
Posted 10 months ago
 This gives an idea In[18]:= Arg[-2 - I # \[Pi]] & /@ Range[10] Out[18]= {-\[Pi] + ArcTan[\[Pi]/2], -\[Pi] + ArcTan[\[Pi]], -\[Pi] + ArcTan[(3 \[Pi])/2], -\[Pi] + ArcTan[2 \[Pi]], -\[Pi] + ArcTan[(5 \[Pi])/2],-\[Pi] + ArcTan[3 \[Pi]], -\[Pi] + ArcTan[(7 \[Pi])/2], -\[Pi] + ArcTan[4 \[Pi]],-\[Pi] + ArcTan[(9 \[Pi])/2], -\[Pi] + ArcTan[5 \[Pi]]} but here you see a rational positive k does it as well In[24]:= FindInstance[Arg[-2 - I k \[Pi]] == -\[Pi] + ArcTan[k \[Pi]/2], {k}] Out[24]= {{k -> 106/5}} why not compute it directly, it's just plane trigonometry.