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73 lines
1.9 KiB
Markdown
73 lines
1.9 KiB
Markdown
# [537. Complex Number Multiplication](https://leetcode.com/problems/complex-number-multiplication/)
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## 题目
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Given two strings representing two [complex numbers](https://en.wikipedia.org/wiki/Complex_number).
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You need to return a string representing their multiplication. Note i2 = -1 according to the definition.
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**Example 1**:
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```
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Input: "1+1i", "1+1i"
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Output: "0+2i"
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Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.
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```
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**Example 2**:
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```
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Input: "1+-1i", "1+-1i"
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Output: "0+-2i"
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Explanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.
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```
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**Note**:
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1. The input strings will not have extra blank.
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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**.
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## 题目大意
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给定两个表示复数的字符串。返回表示它们乘积的字符串。注意，根据定义 i^2 = -1 。
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注意:
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- 输入字符串不包含额外的空格。
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- 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。
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## 解题思路
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- 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。
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- 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。
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## 代码
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```go
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package leetcode
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import (
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"strconv"
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"strings"
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)
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func complexNumberMultiply(a string, b string) string {
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realA, imagA := parse(a)
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realB, imagB := parse(b)
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real := realA*realB - imagA*imagB
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imag := realA*imagB + realB*imagA
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return strconv.Itoa(real) + "+" + strconv.Itoa(imag) + "i"
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}
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func parse(s string) (int, int) {
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ss := strings.Split(s, "+")
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r, _ := strconv.Atoi(ss[0])
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i, _ := strconv.Atoi(ss[1][:len(ss[1])-1])
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return r, i
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}
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``` |