Return to Answer

added 6 characters in body

Source Link

edited Mar 10 at 11:37

These are all complex solutions. There might be more if we take ArcSin and ArcCos as multi-functionsmultivalued functions.

sol = {9/5 - (2 I Sqrt[11])/5, 
   1/5 - (2 I)/5, -1, -3 - (2 I)/Sqrt[5], -(23/5) - (2 I Sqrt[19])/5, 
   9/5 + (2 I Sqrt[11])/5, 
   1/5 + (2 I)/5, -(9/5), -3 + (2 I)/Sqrt[5], -(23/5) + (
    2 I Sqrt[19])/5};

With[{x = a + I b}, 
 ContourPlot[{Re[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0, 
   Im[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0}, {a, -10, 
   10}, {b, -4, 4}, PlotPoints -> 100, Epilog -> Point@(ReIm /@ sol)]]

These are all complex solutions. There might be more if we take ArcSin and ArcCos as multi-functions.

sol = {9/5 - (2 I Sqrt[11])/5, 
   1/5 - (2 I)/5, -1, -3 - (2 I)/Sqrt[5], -(23/5) - (2 I Sqrt[19])/5, 
   9/5 + (2 I Sqrt[11])/5, 
   1/5 + (2 I)/5, -(9/5), -3 + (2 I)/Sqrt[5], -(23/5) + (
    2 I Sqrt[19])/5};

With[{x = a + I b}, 
 ContourPlot[{Re[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0, 
   Im[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0}, {a, -10, 
   10}, {b, -4, 4}, PlotPoints -> 100, Epilog -> Point@(ReIm /@ sol)]]

These are all complex solutions. There might be more if we take ArcSin and ArcCos as multivalued functions.

sol = {9/5 - (2 I Sqrt[11])/5, 
   1/5 - (2 I)/5, -1, -3 - (2 I)/Sqrt[5], -(23/5) - (2 I Sqrt[19])/5, 
   9/5 + (2 I Sqrt[11])/5, 
   1/5 + (2 I)/5, -(9/5), -3 + (2 I)/Sqrt[5], -(23/5) + (
    2 I Sqrt[19])/5};

With[{x = a + I b}, 
 ContourPlot[{Re[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0, 
   Im[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0}, {a, -10, 
   10}, {b, -4, 4}, PlotPoints -> 100, Epilog -> Point@(ReIm /@ sol)]]

Source Link

created Mar 10 at 11:30

three777

These are all complex solutions. There might be more if we take ArcSin and ArcCos as multi-functions.

sol = {9/5 - (2 I Sqrt[11])/5, 
   1/5 - (2 I)/5, -1, -3 - (2 I)/Sqrt[5], -(23/5) - (2 I Sqrt[19])/5, 
   9/5 + (2 I Sqrt[11])/5, 
   1/5 + (2 I)/5, -(9/5), -3 + (2 I)/Sqrt[5], -(23/5) + (
    2 I Sqrt[19])/5};

With[{x = a + I b}, 
 ContourPlot[{Re[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0, 
   Im[2 ArcCos[Sin[Pi*x]] - Pi*Cos[ArcSin[x + 1]]] == 0}, {a, -10, 
   10}, {b, -4, 4}, PlotPoints -> 100, Epilog -> Point@(ReIm /@ sol)]]