# croots.py
# the croots() function is by Tim Peters of the tutors list and much other fame

def getComplexNumberFromUser():
    c = raw_input("Enter either a complex number in form x + yj, or a real number: ")
    if "j" not in c:
        c = eval(c + "+0j")
    else:
        c = eval(c)
    n = int(raw_input("Enter an integer n, to find the n'th roots of that number: "))
    print "c is %s; n is %d" % (c,n)
    return c, n

def croots(c, n):
    """Return list of the n n'th roots of complex c."""
    from math import sin, cos, atan2, pi
    arg = abs(c)**(1.0/n)
    theta = atan2(c.imag, c.real)
    result = []
    for i in range(n):
        theta2 = (theta + 2*pi*i)/n
        x = arg * cos(theta2)
        y = arg * sin(theta2)
        result.append(complex(x, y))
    return result
  
def testCrootsResult(rootsList):
    power = len(rootsList)
    for i in range(power):
        print "root%d is %s" % (i+1,rootsList[i])
        print "root%d to the %d power is %s" % (i+1,power, rootsList[i]**power)
        print

c, n = getComplexNumberFromUser()
rootsList = croots(c, n)
print
testCrootsResult(rootsList)