复数的模数

原文:https://www.geeksforgeeks.org/modulus-of-a-complex-number/

给定一个复数 z ，任务是确定这个复数的模。

注:给定复数 z = a + ib 模量用 |z| 表示，定义为

示例:

输入:z = 3+4i T3】输出:5 | z | =(3²+4²)^1/2=(9+16)^1/2= 5

输入:z = 6–8i 输出: 10 解释: | z | =(6²+(-8)²)^1/2=(36+64)^1/2= 10

方法:对于给定的复数 z = x + iy :

1. 分别求实部和虚部，x 和 y。

   ``` If z = x +iy

   Real part = x Imaginary part = y

   ```

2. 分别求 x 和 y 的平方。

   ``` Square of Real part = x2 Square of Imaginary part = y2

   ```

3. 求计算的平方和。

   ``` Sum = Square of Real part + Square of Imaginary part = x2 + y2

   ```

4. 求计算总和的平方根。这将是给定复数的模数

以下是上述方法的实现:

C++

// C++ program to find the
// Modulus of a Complex Number

#include <bits/stdc++.h>
using namespace std;

// Function to find modulus
// of a complex number
void findModulo(string s)
{
    int l = s.length();
    int i, modulus = 0;

    // Storing the index of '+'
    if (s.find('+') < l) {
        i = s.find('+');
    }
    // Storing the index of '-'
    else {
        i = s.find('-');
    }

    // Finding the real part
    // of the complex number
    string real = s.substr(0, i);

    // Finding the imaginary part
    // of the complex number
    string imaginary = s.substr(i + 1, l - 1);

    int x = stoi(real);
    int y = stoi(imaginary);

    cout << sqrt(x * x + y * y) << "\n";
}

// Driver code
int main()
{
    string s = "3+4i";

    findModulo(s);

    return 0;
}

Java 语言(一种计算机语言，尤用于创建网站)

// Java program to find the
// Modulus of a Complex Number
import java.util.*;

class GFG{

// Function to find modulus
// of a complex number
static void findModulo(String s)
{
    int l = s.length();
    int i, modulus = 0;

    // Storing the index of '+'
    if (s.contains("+")) {
        i = s.indexOf("+");
    }

    // Storing the index of '-'
    else {
        i = s.indexOf("-");
    }

    // Finding the real part
    // of the complex number
    String real = s.substring(0, i);

    // Finding the imaginary part
    // of the complex number
    String imaginary = s.substring(i + 1, l-1);

    int x = Integer.parseInt(real);
    int y = Integer.parseInt(imaginary);

    System.out.print(Math.sqrt(x * x + y * y)+ "\n");
}

// Driver code
public static void main(String[] args)
{
    String s = "3+4i";

    findModulo(s);
}
}

// This code is contributed by Rajput-Ji

Python 3

# Python 3 program to find the
# Modulus of a Complex Number
from math import sqrt

# Function to find modulus
# of a complex number
def findModulo(s):
    l = len(s)
    modulus = 0

    # Storing the index of '+'
    if ( '+' in s ):
        i = s.index('+')

    # Storing the index of '-'
    else:
        i = s.index('-')

    # Finding the real part
    # of the complex number
    real = s[0:i]

    # Finding the imaginary part
    # of the complex number
    imaginary = s[i + 1:l - 1]

    x = int(real)
    y = int(imaginary)

    print(int(sqrt(x * x + y * y)))

# Driver code
if __name__ == '__main__':
    s = "3+4i"

    findModulo(s)

# This code is contributed by Surendra_Gangwar

C

// C# program to find the
// Modulus of a Complex Number
using System;

public class GFG{

// Function to find modulus
// of a complex number
static void findModulo(String s)
{
    int l = s.Length;
    int i;

    // Storing the index of '+'
    if (s.Contains("+")) {
        i = s.IndexOf("+");
    }

    // Storing the index of '-'
    else {
        i = s.IndexOf("-");
    }

    // Finding the real part
    // of the complex number
    String real = s.Substring(0, i);

    // Finding the imaginary part
    // of the complex number
    String imaginary = s.Substring(i + 1, l-i - 2);

    int x = Int32.Parse(real);
    int y = Int32.Parse(imaginary);

    Console.Write(Math.Sqrt(x * x + y * y)+ "\n");
}

// Driver code
public static void Main(String[] args)
{
    String s = "3+4i";

    findModulo(s);
}
}
// This code contributed by sapnasingh4991

Output:

5

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