An advanced civilization is found on a planet 1000 light years away. If we send out a radio wave today, what is the minimum amount of time it would take for us to hear back neglecting the relative motion between the planet and the Earth?

2000 light year

Explanation:

Advanced civilization is 1000 light-years away

1  light-year is the distance traveled by light in 1 earth year i.e. 365 days  with the speed of light i.e.

If civilization is 1000 light-years away then it would take 1000 year  to reach there and another 1000 year to come back to earth (If all other factors remain constant)

So totally it would take 2000 light-year to hear out the radio wave.

wavelength divides in half and speed stays the same.