complex-number-multiplication.py

# Time:  O(1)
# Space: O(1)

# Given two strings representing two complex numbers.
#
# You need to return a string representing their multiplication. Note i2 = -1 according to the definition.
#
# Example 1:
# Input: "1+1i", "1+1i"
# Output: "0+2i"
# Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.
# Example 2:
# Input: "1+-1i", "1+-1i"
# Output: "0+-2i"
# Explanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.
# Note:
#
# The input strings will not have extra blank.
# The input strings will be given in the form of a+bi,
# where the integer a and b will both belong to the range of [-100, 100].
# And the output should be also in this form.

class Solution(object):
    def complexNumberMultiply(self, a, b):
        """
        :type a: str
        :type b: str
        :rtype: str
        """
        ra, ia = map(int, a[:-1].split('+'))
        rb, ib = map(int, b[:-1].split('+'))
        return '%d+%di' % (ra * rb - ia * ib, ra * ib + ia * rb)