q.is_real() for some symbolic q produce erroneous results

[maxale]

Initially I thought that q.is_real() is equivalent to q.imag().is_zero(), both of which can produce erroneous results as I reported in #38586. However, it turns out that each of them may produce an incorrect result independently of the other. Hence, I separate the issue with .is_real() here.

In the following example r.imag().is_zero() gives correct True while r.is_real() gives incorrect False:

r = -1/2056*sqrt(2)*(-231043*sqrt(2) + 1682065/4)^(1/4)*cos(1/2*arctan(1/2*sqrt(-67260300684*sqrt(2) + 97845815881)/(38051*sqrt(2) + 20432)))
print( r.n() )
print( r.imag().is_zero() )
print( r.is_real() )

Output:

-0.0118652163874385
True
False

This code was originally posted in #38586 (comment)