janhardo

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11 years, 254 days
B. Ed math

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Best wishes for all for the New Year 2022!

Is it possible to search for my questions who answered this on Maple Primes ?

Colored axes and showing 5 colored branches (Riemann surfaces) and ln(z)  as a spiral

There is a plotcompare(log(z), expression_plot, 3); branches(ln);

FunctionAdvisor(branch_cuts, log(z));
                         [ln(z), z < 0]

The principal branch is the red colored one : Pi..-Pi (difficult to see here )


                                       pic 1

Compare this pic 1  with the Imaginaire plot log(z) in plotcompare command.

As maple 1d input:

expr:=(1/2)*a*(b/c)/d;     

As 2 d input : 

This rightside of the equation i like to get in Maple , but how?

answer

  • How to get the ln(z) 3d plot example in the FunctionAdvisor /plot ?
  • a table plot, to show different plots together 

 

Some more difficult calculation with complex numbers

Starting from the equation     
A = arctan(z/b)/b and arctan(z/b)/b = int(1/(b^2+z^2), z = 0 .. z)
made the substitution                               
z = i*b(t-1)/(t+1)
Thus obtaining NULL
A = -(int(1/t, t = 1 .. t))/(2*bi) and -(int(1/t, t = 1 .. t))/(2*bi) = log[10](t)/(2*bi) and log[10](t)/(2*bi) = log[10]((b*i+z)/(b*i-z))/(2*bi)
One of the important relations between logarithms and inverse trigonometrische functions

Download logaritmisc_functie_betrekking_goniometrische_functie.mw

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