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program complex_solutions
! print some complex solutions to the equation: 1**x = rhs.
use, intrinsic :: iso_fortran_env, only: wp=>real64
implicit none
complex(wp) :: z1, arg, x
real(wp), parameter :: rhs = 4.0_wp, twopi = 8 * atan(1.0_wp), lnrhs = log(rhs), tol = 1.0e-12_wp
integer :: k
character(*), parameter :: cfmth='("Complex solutions to 1**x=",g0.4/a2,*(4x,a11,5x))', &
& cfmt='(i2,*(" (",es0.2,",",es0.2,")":))'
write(*,cfmth) rhs, 'k', 'arg=i2Pik', 'exp(arg)', 'x', 'exp(arg)**x', 'exp(arg*x)'
do k = 1, 10
arg = cmplx(0.0_wp, twopi * k, kind=wp)
z1 = exp(arg)
x = cmplx(0.0_wp, -lnrhs/(twopi*k), kind=wp)
! Check for correctness:
if (abs(real(exp(arg*x)) - rhs) > tol .or. abs(aimag(exp(arg*x))) > tol) then
print *, "Integration test failed for k=", k
error stop 1
end if
write(*,cfmt) k, arg, z1, x, z1**x, exp(arg*x)
end do
end program complex_solutions
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