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Question: implicit plot a complex function

Question:implicit plot a complex function

mehdi jafari 749 Maple
implicitplot plotting
February 10 2020
0

i have a function which contains Ln and arctan fanctions in which the output function is complex.
how can i implicitplot this complex function? tnx for the help
 

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restart
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with(plots, implicitplot)
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ode := diff(y(w), w)+(sqrt((12*Pi)(y(w)^2+m^2*w^2))*y(w)+m^2*w)/y(w) = 0

diff(y(w), w)+(2*3^(1/2)*Pi(y(w)^2+m^2*w^2)^(1/2)*y(w)+m^2*w)/y(w) = 0

 (1)
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Ans := dsolve([ode])

[{ln(w)+(1/4)*ln(-m^4-2*m^2*y(w)^2/w^2-y(w)^4/w^4+12*y(w)^2*Pi/w^2)-(3/2)*arctan((1/4)*(-2*m^2-2*y(w)^2/w^2+12*Pi)/(3*Pi*m^2-9*Pi^2)^(1/2))*Pi/(3*Pi*m^2-9*Pi^2)^(1/2)+(1/4)*ln(2*Pi^(1/2)*3^(1/2)*y(w)/w-y(w)^2/w^2-m^2)-(3/2)*arctan((1/2)*(2*Pi^(1/2)*3^(1/2)-2*y(w)/w)/(m^2-3*Pi)^(1/2))/((3*m^2-9*Pi)/Pi)^(1/2)-(1/4)*ln(2*Pi^(1/2)*3^(1/2)*y(w)/w+m^2+y(w)^2/w^2)+(3/2)*arctan((1/2)*(2*y(w)/w+2*Pi^(1/2)*3^(1/2))/(m^2-3*Pi)^(1/2))/((3*m^2-9*Pi)/Pi)^(1/2)-_C1 = 0}]

 (2)
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P:=subs(y(w)=Y,eval(lhs(Ans[1, 1]), [_C1 = 0, m = 1]))

ln(w)+(1/4)*ln(-1-2*Y^2/w^2-Y^4/w^4+12*Y^2*Pi/w^2)-(3/2)*arctan((1/4)*(-2-2*Y^2/w^2+12*Pi)/(-9*Pi^2+3*Pi)^(1/2))*Pi/(-9*Pi^2+3*Pi)^(1/2)+(1/4)*ln(2*Pi^(1/2)*3^(1/2)*Y/w-Y^2/w^2-1)-(3/2)*arctan((1/2)*(2*Pi^(1/2)*3^(1/2)-2*Y/w)/(1-3*Pi)^(1/2))/((-9*Pi+3)/Pi)^(1/2)-(1/4)*ln(2*Pi^(1/2)*3^(1/2)*Y/w+1+Y^2/w^2)+(3/2)*arctan((1/2)*(2*Y/w+2*Pi^(1/2)*3^(1/2))/(1-3*Pi)^(1/2))/((-9*Pi+3)/Pi)^(1/2)

 (3)
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implicitplot(P,w=-10..0,Y=0..10)

 
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evalf((eval(P,[w=1,Y=1])))

1.655474573+.8307038310*I

 (4)
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