You want to iterate over elements of a list and apply the sqrt function on it so. You can use the built-in function map which will apply the first argument to every elements of the second:

Copylst = [-1, 3, -8]
results = map(cmath.sqrt, lst)

Another way is with the classic list comprehension:

Copylst = [-1, 3, -8]
results = [cmath.sqrt(x) for x in lst]

Execution example:

Copy>>> lst = [-4, 3, -8, -9]
>>> map(cmath.sqrt, lst)
[2j, (1.7320508075688772+0j), 2.8284271247461903j, 3j]
>>> [cmath.sqrt(x) for x in lst]
[2j, (1.7320508075688772+0j), 2.8284271247461903j, 3j]

If you're using Python 3, you may have to apply list() on the result of map (or you'll have a ietrator object)

Shifting this discussion from the comments...

In Python 3.0 the behaviour of the power operator changed. In earlier versions of python, raising a negative number to a fractional power raised a ValueError exception, but in Python 3 it yields a complex result.

An alternative for finding the square root is the python is the math.sqrt function. In Python 3 this raises a ValueError exception when used with a negative number:

Python 3.4.3 (v3.4.3:9b73f1c3e601, Feb 24 2015, 22:43:06) [MSC v.1600 32 bit (Intel)] on win32
Type "help", "copyright", "credits" or "license" for more information.
>>> import math
>>> math.sqrt(-200)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: math domain error

To avoid the invalid value warning/error, the argument to numpy's sqrt function must be complex:

In [8]: import numpy as np

In [9]: np.sqrt(-1+0j)
Out[9]: 1j

As @AshwiniChaudhary pointed out in a comment, you could also use the cmath standard library:

In [10]: cmath.sqrt(-1)
Out[10]: 1j