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/* * 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; } // 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); } /** Compute the product of a complex number and a real number. * * @param a The real number to be multiplied. * @return A new complex number which is the product. */ public Complex mult(double a) { return new Complex(a*x,a*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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