leetcode-537-Complex-Number-Multiplication

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描述

Given two strings representing two complex numbers.

You need to return a string representing their multiplication. Note $i^2 = -1$ according to the definition.

Example 1:

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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:

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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.

分析

复数相乘，挺简单的。$(a+bi)*(c+di)=ac+bci+adi-bd=(ac-db)+(ad+bc)i$

解决方案1(Java)

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class Solution {
    public String complexNumberMultiply(String a, String b) {
        String aList[] = a.split("\\+|i");
        String bList[] = b.split("\\+|i");
        int aReal = Integer.parseInt(aList[0]);
        int aImg = Integer.parseInt(aList[1]);
        int bReal = Integer.parseInt(bList[0]);
        int bImg = Integer.parseInt(bList[1]);
        return (aReal*bReal - aImg*bImg) + "+" + (aReal*bImg + aImg*bReal) + "i";
    }
}

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