537. Complex Number Multiplication 复数乘法运算

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:

1. The input strings will not have extra blank.
2. 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.

# 设z1=a+bi，z2=c+di(a、b、c、d∈R)是任意两个复数
# 那么它们的积(a+bi)(c+di)=(ac-bd)+(bc+ad)i.
class Solution(object):
    def complexNumberMultiply(self, a, b):
        import re
        pattern = re.compile("-*d+")
        numA = int(pattern.findall(a)[0])
        numB = int(pattern.findall(a)[1])
        numC = int(pattern.findall(b)[0])
        numD = int(pattern.findall(b)[1])
        real = numA * numC - numB * numD
        imaginary = numB * numC + numA * numD
        return str(real) + "+" + str(imaginary) + "i"

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