# Source code for Complex.java

What follows is the highlighted source code with comments. You can also download this file directly: Complex.java.

```/*
* This work by W. Patrick Hooper is free of known copyright restrictions.
* The work is in the public domain.
*
* Author's website: <a href="http://wphooper.com">http://wphooper.com</a>.
*/

package number;

/**
* This class stores a complex number, and allows the user to do arithmetic
* with these numbers.
*
* Note that our complex numbers are immutable. That is, once they are
* constructed, they will not change. In particular, all our algebraic
* operations create a new complex number rather than updating the current one.
*
* @author W. Patrick Hooper
*/
public final class Complex {
// The number stored is x+I*y.
final private double x, y;
// I don't want to allow anyone to access these numbers so I've labeled
// them private.

/** Construct a point from real and imaginary parts. */
public Complex(double real_part, double imaginary_part) {
x=real_part;
y=imaginary_part;
}

/** Construct a real number. */
public Complex(double real_part) {
x=real_part;
y=0;
}

// A static constructor.

/** Construct a complex number from the given polar coordinates. */
public static Complex fromPolar(double r, double theta) {
return new Complex(r*Math.cos(theta), r*Math.sin(theta));
}

// Basic operations on Complex numbers.

/** Return the real part. */
public double re(){
return x;
}

/** Return the imaginary part. */
public double im(){
return y;
}

/** Return the complex conjugate */
public Complex conj() {
return new Complex(x,-y);
}

/** Return the square of the absolute value. */
public double absSquared() {
return x*x+y*y;
}

/** Return the absolute value. */
public double abs() {
// The java.lang.Math package contains many useful mathematical functions,
// including the square root function.
return Math.sqrt(absSquared());
}

// ARITHMETIC

/** Add a complex number to this one.
*
* @param z The complex number to be added.
* @return A new complex number which is the sum.
*/
public Complex add(Complex z) {
return new Complex(x+z.x, y+z.y);
}

/** Subtract a complex number from this one.
*
* @param z The complex number to be subtracted.
* @return A new complex number which is the sum.
*/
public Complex minus(Complex z) {
return new Complex(x-z.x, y-z.y);
}

/** Negate this complex number.
*
* @return The negation.
*/
public Complex neg() {
return new Complex(-x, -y);
}

/** Compute the product of two complex numbers
*
* @param z The complex number to be multiplied.
* @return A new complex number which is the product.
*/
public Complex mult(Complex z) {
return new Complex(x*z.x-y*z.y, x*z.y+z.x*y);
}

/** Divide this complex number by a real number.
*
* @param q The number to divide by.
* @return A new complex number representing the quotient.
*/
public Complex div(double q) {
return new Complex(x/q,y/q);
}

/** Return the multiplicative inverse. */
public Complex inv() {
// find the square of the absolute value of this complex number.
double abs_squared=absSquared();
return new Complex(x/abs_squared, -y/abs_squared);
}

/** Compute the quotient of two complex numbers.
*
* @param z The complex number to divide this one by.
* @return A new complex number which is the quotient.
*/
public Complex div(Complex z) {
return mult(z.inv());
}

/** Return the complex exponential of this complex number. */
public Complex exp() {
return new Complex(Math.exp(x)*Math.cos(y),Math.exp(x)*Math.sin(y));
}

// FUNCTIONS WHICH KEEP JAVA HAPPY:

/** Returns this point as a string.
* The main purpose of this function is for printing the string out,
* so we return a string in a (fairly) human readable format.
*/
// The _optional_ override directive "@Override" below just says we are
// overriding a function defined in a parent class. In this case, the
// parent is java.lang.Object. All classes in Java have the Object class
// as a superclass.
@Override
public String toString() {
// Comments:
// 1) "" represents the empty string.
// 2) If you add something to a string, it converts the thing you
// are adding to a string, and then concatentates it with the string.

// We do some voodoo to make sure the number is displayed reasonably.
if (y==0) {
return ""+x;
}
if (y>0) {
return ""+x+"+"+y+"*I";
}
// otherwise y<0.
return ""+x+"-"+(-y)+"*I";
}

/** Return true if the object is a complex number which is equal to this complex number. */
@Override
public boolean equals(Object obj) {
// Return false if the object is null
if (obj == null) {
return false;
}
// Return false if the object is not a Complex number
if (!(obj instanceof Complex)) {
return false;
}

// Now the object must be a Complex number, so we can convert it to a
// Complex number.
Complex other = (Complex) obj;

// If the x-coordinates are not equal, then return false.
if (x != other.x) {
return false;
}
// If the y-coordinates are not equal, then return false.
if (y != other.y) {
return false;
}
// Both parts are equal, so return true.
return true;
}

// Remark: In Java, we should really override the hashcode function
// whenever we override the equals function. But, I don't want to
// get into this for a light introduction to programming in java.
// Hash codes are necessary for various of Java's collections. See HashSet for instance.
// The following was generated by Netbeans.
@Override
public int hashCode() {
int hash = 3;
hash = 83 * hash + (int) (Double.doubleToLongBits(this.x) ^ (Double.doubleToLongBits(this.x) >>> 32));
hash = 83 * hash + (int) (Double.doubleToLongBits(this.y) ^ (Double.doubleToLongBits(this.y) >>> 32));
return hash;
}
}
```
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Last modified on August 17, 2018.
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