#!/usr/bin/env python3
#
#       This program is free software; you can redistribute it and/or modify
#       it under the terms of the GNU General Public License as published by
#       the Free Software Foundation; either version 3 of the License, or
#       (at your option) any later version.
#
#       This program is distributed in the hope that it will be useful,
#       but WITHOUT ANY WARRANTY; without even the implied warranty of
#       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#       GNU General Public License for more details.
#
#       You should have received a copy of the GNU General Public License
#       along with this program; if not, write to the Free Software
#       Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
#       MA 02110-1301, USA.

## modified get_int() for this program to print examples if 'enter'
def get_int(msg, printd):
    while True:
        i = input(msg)
        try:
            if i:
                i = int(i)
                return(i)
            else:
                print(printd)
                break
        except ValueError as err:
            print(err)
            continue

def remainder(exponent):
    r = (exponent / 4) - (exponent // 4)
    if r == 0.25:
        return 1
    elif r == 0.5:
        return 2
    elif r == 0.75:
        return 3
    elif r == float(0):
        return 4

def print_simp(exponent, remainder):
    if remainder == 1:
        p = "i^1"
        a = "i"
    elif remainder == 2:
        p = "i^2"
        a = "-1"
    elif remainder == 3:
        p = "i^3"
        a = "-i"
    elif remainder == 4:
        p = "i^4"
        a = "1"
    print("i^{0} = {1} = {2}".format(exponent, p, a))

def main():
    print("Simplify a complex number, type a number as the exponent, or 'enter' for examples. \nUse ^C to exit.")
    printd = "i^1 = i \ni^2 = -1 \ni^3 = -i \ni^4 = 1"
    while True:
        try:
            e = get_int("i\u207F ", printd)
            if e is not None:
                print_simp(e, remainder(e))
        except KeyboardInterrupt:
            print()
            break

if __name__ == "__main__":
    main()