When you're evaluating -12**2 you're essentially evaluating -(12**2).

And also, (-12) squared is always 144.

If you want to retain the sign use -(12**2). If you don't want the sign to be retained, use (-12)**2

If you're trying to evaluate the square root of a negative number. It is going to be the same as the sqrt of the positive number multiplied by imaginary i

Just evaluate negative numbers the same way you would positive numbers, and append i to it.

In your particular case, the min function is screwing things up when you evalute negative numbers

Perhaps you would accomplish this with something to the effect of

text = raw_input("please give 2 numbers to multiply separated with a comma:")
split_text = text.split(',')
a = int(split_text[0])
b = int(split_text[1])
# The last three lines could be written: a, b = map(int, text.split(','))
# but you may find the code I used a bit easier to understand for now.

if b > 0:
    num_times = b
else:
    num_times = -b

total = 0
# While loops with counters basically should not be used, so I replaced the loop 
# with a for loop. Using a while loop at all is rare.
for i in xrange(num_times):
    total += a 
    # We do this a times, giving us total == a * abs(b)

if b < 0:
    # If b is negative, adjust the total to reflect this.
    total = -total

print total

or maybe

a * b

I couldn't find anything about it in the Python style guide, as you said, but searching for "unary operator spacing" brought more hits from various languages, such as this for Javascript:

No space should separate a unary operator and its operand except when the operator is a word such as typeof.

Or this for C:

Don't use spaces around unary operators, except sizeof and casts

In the Linux kernel:

Use one space around (on each side of) most binary and ternary operators, [...] but no space after unary operators:

Note that a writing style for code, which is usually written with a fixed-width font and mostly Latin characters, is quite different than that for equations, where you can find both latin and greek letters, topological constructs such as fractions or those marks surrounding that epsilon you have there, and other things that make them a whole lot more complex than code.