0537. Complex Number Multiplication

# 537. Complex Number Multiplication#

## 题目 #

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.

## 题目大意 #

• 输入字符串不包含额外的空格。
• 输入字符串将以 a+bi 的形式给出，其中整数 a 和 b 的范围均在 [-100, 100] 之间。输出也应当符合这种形式。

## 解题思路 #

• 给定 2 个字符串，要求这两个复数的乘积，输出也是字符串格式。
• 数学题。按照复数的运算法则，i^2 = -1，最后输出字符串结果即可。

## 代码 #

``````
package leetcode

import (
"strconv"
"strings"
)

func complexNumberMultiply(a string, b string) string {
realA, imagA := parse(a)
realB, imagB := parse(b)
real := realA*realB - imagA*imagB
imag := realA*imagB + realB*imagA
return strconv.Itoa(real) + "+" + strconv.Itoa(imag) + "i"
}

func parse(s string) (int, int) {
ss := strings.Split(s, "+")
r, _ := strconv.Atoi(ss[0])
i, _ := strconv.Atoi(ss[1][:len(ss[1])-1])
return r, i
}

``````

Sep 6, 2020