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How can I graph the area.

Posted 1 month ago
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How can I graph the area described by the expression

Im[R Cos[x/2]^2] + Re[R Sin[x]] != Im[R Sin[x/2]^2] || 
 Re[R Cos[x/2]^2] < Im[R Sin[x]] + Re[R Sin[x/2]^2] || 
 1 + Im[R Sin[x]] + Re[R Sin[x/2]^2] < Re[R Cos[x/2]^2]

? x is polar angle and R is the radius in polar coordinates.

POSTED BY: h r
Answer
3 Replies

If R and x are real numbers, what is the purpose of Re and Im in the formulas?

Posted 1 month ago

A symbolic integration operation returned a solution in a region limited by this formula. I don't know why the formula includes Im number.

POSTED BY: h r
Answer

You can give relevant assumptions to a symbolic integration. However, your region is very simple to describe: it is the whole plane except for a segment:

myRegion = 
  Simplify[(Im[R Cos[x/2]^2] + Re[R Sin[x]] != Im[R Sin[x/2]^2] || 
     Re[R Cos[x/2]^2] < Im[R Sin[x]] + Re[R Sin[x/2]^2] || 
     1 + Im[R Sin[x]] + Re[R Sin[x/2]^2] < Re[R Cos[x/2]^2]), 
   Element[x | R, Reals]];
Reduce[myRegion && 0 <= x < 2 Pi && R >= 0, {x, R}, Reals]
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