Thread: Complex Number Calculations

Problem: A complex number is defined as z=a+i*b, where a is the real part, and b is the imaginary part. In other words, in order to define a complex number, we need the two floating numbers a and b.

Write methods that perform for each of the following operations with complex numbers z1 = a1 + i*b1, and z2 = a2 + i*b2:

Addition: z1 + z2=(a1+a2) + i*(b1+b2)
Subtraction: z1 - z2=(a1-a2) + i*(b1-b2)
Multiplication: z1*z2 = (a1*a2 – b1*b2) + i*(a1*b2 + b1*a2)
Division: z1/z2 = (a1*a2 +b1*b2)/(a2^2 + b2^2) + i*(b1*a2 – a1*b2)/(a2^2 + b2^2)
Create a test program that asks for the real and imaginary parts of two complex numbers from the user, and displays the results of the four operations, writing the formula as shown above, and replacing the a1, a2, b1 and b2 with the numbers entered by the user.

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The professor used the incorrect complex number equations and has notified the students of his error. I have run into a few problems thus far.

1. I'm not sure how to use floating numbers with the Math.pow(double, double) function, since its requires doubles!? So instead of using floating numbers, I've knowingly switched them all to double in order to see if the code itself is working properly for the purposes of this forum. Is there a way that I can modify this function so that it will work for floating numbers?

2. Regarding the division method, an error stating that c and d have not been initialized and I'm not sure how to change it because the other calculation methods work fine. Why do I need to initialize c and d in the division method and not the others?

3. Am I on the right path? I have surfed the web to see how others completed the program and they all appear very different than mine...

4. As always feel free to offer an constructive criticism on how I can improve on the code. It's always important to me that I create an easy to read and streamlined program. I'm just beginning my journey into programming, so please be critical! Thank you.
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package program5;
 
import java.util.Scanner;
 
public class Program5 {
 
    static double a, b, c, d;
    static double i = Math.pow(-1,1/2);
 
    public static void main(String[] args) {
 
        Scanner input = new Scanner(System.in);
        System.out.println(" + Calculating Complex Numbers + ");
        System.out.printf("%15s\n","z = a + (i*b) and z = c + (i*d)");
        System.out.print("Enter a: ");
        a = input.nextFloat();       
        System.out.print("Enter b: ");
        b = input.nextFloat();
        System.out.print("Enter c: ");
        c = input.nextFloat();
        System.out.print("Enter d: ");
        d = input.nextFloat();
 
        addition("Addition: ");
        subtraction("Subtraction: ");
        multiplication("Multiplication: ");
        division("Division: ");
    }
    public static void addition(String name){
        double add = (a + c) + i*(b + d);
        System.out.println(name + add);
    }
    public static void subtraction(String name){
        double subtract = (a - c) + i*(b - d);
        System.out.println(name + subtract);
    }
    public static void multiplication(String name){
        double multiply = ((a * c) - (b * d)) + i*((b * c) + (a * d));
        System.out.println(name + multiply);
    }
    public static void division(String name){
        double c = Math.pow(c,2);
        double d = Math.pow(d,2);
 
        double division = (((a * c) + (b * d)) / (c + d)) + i*((b * c)- 
                          (a * d)) / ((c + d));
        System.out.println(name + division);
    }
}

thank you for the feedback Norm. I used a different formula for the division that didn't involve Math.pow(). I hope that I am doing the right thing here.

 public class Program5 {
 
    static double realA, imagineB, realC, imagineD;
    static double i = Math.pow(-1,1/2);
 
    public static void main(String[] args) {
 
        Scanner input = new Scanner(System.in);
        System.out.println(" + Calculating Complex Numbers + ");
        System.out.printf("%15s\n","z = a + (i*b) and z = c + (i*d)");
        System.out.print("Enter real a: ");
        realA = input.nextFloat();       
        System.out.print("Enter imaginary b: ");
        imagineB = input.nextFloat();
        System.out.print("Enter real c: ");
        realC = input.nextFloat();
        System.out.print("Enter imaginary d: ");
        imagineD = input.nextFloat();
        System.out.println();
 
        addition("Addition: ");
        subtraction("Subtraction: ");
        multiplication("Multiplication: ");
        division("Division: ");
    }
    public static void addition(String name){
        double add = (realA + realC) + i*(imagineB + imagineD);
        System.out.println(name + add);
    }
    public static void subtraction(String name){
        double subtract = (realA - realC) + i*(imagineB - imagineD);
        System.out.println(name + subtract);
    }
    public static void multiplication(String name){
        double multiply = ((realA * realC) - (imagineB * imagineD)) + i*((imagineB * realC)
                + (realA * imagineD));
        System.out.println(name + multiply);
    }
    public static void division(String name){
      //  double imaginaryOne = Math.pow( imagineB , 2);
      //  double imaginaryTwo = Math.pow(imagineD , 2);
 
            double division = ((realA + (imagineB * i)) / (realC + (imagineD * i)));
            System.out.println(name + division);
    }

I still don't think I'm doing something right though by using -1^(1/2) as the value of i. Is this what the professor is asking for?

"Create a test program that asks for the real and imaginary parts of two complex numbers from the user, and displays the results of the four operations, writing the formula as shown above, and replacing the a1, a2, b1 and b2 with the numbers entered by the user."

This is what our professor had to say for the assignment...I just want to make sure I'm comprehending this correctly. I'm concerned bc my code looks very different than others I have looked at online dealing with complex numbers.

PleaseHELP!

You are right, it is redundant to state the obvious with a method that is meant to perform only one function in the program. I think I was just playing around and glad
that it worked when I tried it! ha.

I know what you mean, when there should be a class for it, but there is nothing remotely similar to this concept in our text and its thrown through a loop.

Nevertheless, I've looked through our textbook and surfed the web for information on complex numbers, but my search has not provided a lot. If anybody has a good link on this concept let me know. I've seen a few different programs dealing with " Complex() " but no topic discussing the purpose and use of the function.

I'm not sure what your remaining questions are, but just looking at your latest code I see that you're not quite getting it. The result of the complex number mathematical operations should result in a real and complex component. Your current code prints the result as a single number, but all results should be in the form:

a + b*i

where the values a and b are calculated from the equations given in your first post, though I'm not sure what you meant by mentioning that the professor gave the wrong equation. Was that straightened out? You can refer to this page if you're not sure and for examples of what the results of the operations should look like.

Hope this helps, but ask if you still have questions.

So, I should just use a character variable i instead of assigning i a value of sqrt(-1)? Given that, the code still seems much easier than what I've seen elsewhere on the web. I think I am missing something that deals with Complex()...does that sound correct? I guess I'm justing having a hard time figuring out the purpose of this program---in other words, a basic calculation and that is way too easy.

Yes, but to be clear, let's take addition as an example:

For z1 = a1 + i*b1, and z2 = a2 + i*b2 where

a1 = 1
b1 = 2
a2 = 3
a4 = 4

so:

z1 = 1 + 2i
z2 = 3 + 4i

then

z1 + z2 = 4 + 6i

That's how the answer should look, 4 + 6i, or 4 + 6*i, or whatever variation of that you prefer, but the answer should be an expression with a real and imaginary part.

I can't comment on how your code compares to other code you've seen on the Internet. You haven't shown us what you're talking about, and I've no way to know whether the code you've seen is relevant to your assignment.

As you said, your assignment is pretty simple: get 4 numbers from the user, program the equations correctly, and output the results. How you present or return those results from the methods you've written may be the complex (pun convenient) part of the assignment you haven't conquered yet. You can't return two values from the methods, so you'll have to wrap them in a single object, perhaps the Complex object you've seen elsewhere, an array, or simply output the result from each method. I don't see that it matters based on the assignment and may depend on what you're able to do.

Great! Thank you for the detailed response Mr. Brannon. That really helped to clear things up for me. I was at a cross roads with the output, but I think I can figure it out from here.