Sympy absolute value of complex exponential

Question

When working with complex numbers in polar form, I've experienced a strange behavior. For example, doing

from sympy import *
simplify(Abs(exp(I)))

I would expect the result 1 because the absolute value of a complex exponential should always be one if the exponent is only imaginary. However, sympy gives as answer

Abs(exp(I))

Doing the alternative

phi=symbols('phi', real=True)
y=exp(I*phi)
sqrt(y*conj(y))

gives the expected result but is less clear than abs in my opinion. Did I miss some constraint that prevents sympy from performing this simplification when just using abs?

Well, for what reason? It does also not really matter if the simplify is there or not. — jan, Jun 05 '14 at 14:36

score 5 · Accepted Answer · answered Jun 06 '14 at 21:56

simplify could definitely be smarter about this.

In general, to simplify things using complex numbers, use expand_complex, which tries to rewrite the expression as a + b*I, where a, and b are real. This works for me.

In [17]: (abs(exp(I))).expand(complex=True)
Out[17]:
   ___________________
  ╱    2         2
╲╱  cos (1) + sin (1)

In [18]: simplify(abs(exp(I)).expand(complex=True))
Out[18]: 1

Sympy absolute value of complex exponential

1 Answers1