Create Complex Numbers Utils

DIRECTORY.md

@@ -282,6 +282,7 @@
             * [CircularConvolutionFFT](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/CircularConvolutionFFT.java)
             * [CollatzConjecture](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/CollatzConjecture.java)
             * [Combinations](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/Combinations.java)
+            * [ComplexNumberUtil](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java)
             * [Convolution](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/Convolution.java)
             * [ConvolutionFFT](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/ConvolutionFFT.java)
             * [CrossCorrelation](https://github.com/TheAlgorithms/Java/blob/master/src/main/java/com/thealgorithms/maths/CrossCorrelation.java)
@@ -726,10 +727,12 @@
             * [CeilTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CeilTest.java)
             * [CollatzConjectureTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CollatzConjectureTest.java)
             * [CombinationsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CombinationsTest.java)
+            * [ComplexNumberUtilTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/ComplexNumberUtilTest.java)
             * [CrossCorrelationTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/CrossCorrelationTest.java)
             * [DigitalRootTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/DigitalRootTest.java)
             * [DistanceFormulaTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/DistanceFormulaTest.java)
             * [DudeneyNumberTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/DudeneyNumberTest.java)
+            * [FactorialRecursionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialRecursionTest.java)
             * [FactorialTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FactorialTest.java)
             * [FastInverseSqrtTests](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FastInverseSqrtTests.java)
             * [FFTTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/FFTTest.java)
@@ -762,7 +765,9 @@
             * [MillerRabinPrimalityCheckTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/MillerRabinPrimalityCheckTest.java)
             * [MinValueTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/MinValueTest.java)
             * [MobiusFunctionTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/MobiusFunctionTest.java)
+            * [ModeTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/ModeTest.java)
             * [NthUglyNumberTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/NthUglyNumberTest.java)
+            * [NumberOfDigitsTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/NumberOfDigitsTest.java)
             * [PalindromeNumberTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/PalindromeNumberTest.java)
             * [ParseIntegerTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/ParseIntegerTest.java)
             * [PascalTriangleTest](https://github.com/TheAlgorithms/Java/blob/master/src/test/java/com/thealgorithms/maths/PascalTriangleTest.java)

src/main/java/com/thealgorithms/maths/ComplexNumberUtil.java

@@ -0,0 +1,264 @@
+package com.thealgorithms.maths;
+
+public class ComplexNumberUtil {
+
+    public static class ComplexNumber {
+        public final double REAL;
+        public final double IMAGINARY;
+
+        public ComplexNumber(double real, double imaginary) {
+            REAL = real;
+            IMAGINARY = imaginary;
+        }
+
+        @Override
+        public boolean equals(Object obj) {
+            if (obj instanceof ComplexNumber num) {
+                return this.REAL == num.REAL && this.IMAGINARY == num.IMAGINARY;
+            }
+
+            return super.equals(obj);
+        }
+
+        @Override
+        public String toString() {
+            return REAL + ((IMAGINARY < 0) ? (" - " + Math.abs(IMAGINARY)) : (" + " + IMAGINARY)) + "i";
+        }
+    }
+
+    public static final ComplexNumber ZERO = new ComplexNumber(0, 0);
+    public static final ComplexNumber ONE = new ComplexNumber(1, 0);
+    public static final ComplexNumber TWO = new ComplexNumber(2, 0);
+    public static final ComplexNumber PLUS_I = new ComplexNumber(0, 1);
+    public static final ComplexNumber MINUS_I = new ComplexNumber(0, -1);
+
+    /**
+     * add two complex numbers
+     * @param num1 the first complex number
+     * @param num2 the second complex number
+     * @return the sum of num1 and num2
+     */
+    public static ComplexNumber add(ComplexNumber num1, ComplexNumber num2) {
+        return new ComplexNumber(num1.REAL + num2.REAL, num1.IMAGINARY + num2.IMAGINARY);
+    }
+
+    /**
+     * Subtracts the second complex number from the first complex number.
+     *
+     * @param num1 the first complex number
+     * @param num2 the second complex number
+     * @return the result of subtracting num2 from num1
+     */
+    public static ComplexNumber subtract(ComplexNumber num1, ComplexNumber num2) {
+        return new ComplexNumber(num1.REAL - num2.REAL, num1.IMAGINARY - num2.IMAGINARY);
+    }
+
+    /**
+     * Multiplies two complex numbers.
+     *
+     * @param num1 the first complex number
+     * @param num2 the second complex number
+     * @return the product of num1 and num2
+     * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Multiplication">...</a>
+     */
+    public static ComplexNumber multiply(ComplexNumber num1, ComplexNumber num2) {
+        return new ComplexNumber(num1.REAL * num2.REAL - num1.IMAGINARY * num2.IMAGINARY, num1.REAL * num2.IMAGINARY + num1.IMAGINARY * num2.REAL);
+    }
+
+    /**
+     * Divides the first complex number by the second complex number.
+     *
+     * @param num1 the numerator complex number
+     * @param num2 the denominator complex number
+     * @return the result of dividing num1 by num2
+     * @throws RuntimeException if the divisor (num2) is zero
+     * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Complex_conjugate,_absolute_value_and_argument">...</a>
+     */
+    public static ComplexNumber divide(ComplexNumber num1, ComplexNumber num2) {
+        final double divisor = num2.REAL * num2.REAL + num2.IMAGINARY * num2.IMAGINARY;
+        if (divisor == 0) {
+            throw new RuntimeException("Cannot divide by zero");
+        }
+
+        return new ComplexNumber((num1.REAL * num2.REAL + num1.IMAGINARY * num2.IMAGINARY) / divisor, (num1.IMAGINARY * num2.REAL - num1.REAL * num2.IMAGINARY) / divisor);
+    }
+
+    /**
+     * Computes the absolute value (magnitude) of a complex number.
+     *
+     * @param num the complex number
+     * @return the absolute value of num
+     * @link <a href="https://en.wikipedia.org/wiki/Complex_number#Complex_conjugate,_absolute_value_and_argument">...</a>
+     */
+    public static double abs(ComplexNumber num) {
+        return Math.sqrt(num.REAL * num.REAL + num.IMAGINARY * num.IMAGINARY);
+    }
+
+    /**
+     * Computes the exponential function of a complex number.
+     *
+     * @param num the complex number
+     * @return e raised to the power of num
+     * @link <a href="https://en.wikipedia.org/wiki/Exponential_function#Continued_fractions_for_ex">...</a>
+     */
+    public static ComplexNumber exp(ComplexNumber num) {
+        final double coefficient = Math.exp(num.REAL);
+        return new ComplexNumber(coefficient * Math.cos(num.IMAGINARY), coefficient * Math.sin(num.IMAGINARY));
+    }
+
+    /**
+     * Computes the natural logarithm of a complex number.
+     *
+     * @param num the complex number
+     * @return the natural logarithm of num
+     * @throws RuntimeException if num is zero
+     * @link <a href="https://en.wikipedia.org/wiki/Complex_logarithm#Calculating_the_principal_value">...</a>
+     */
+    public static ComplexNumber ln(ComplexNumber num) {
+        if (num.equals(ZERO)) {
+            throw new RuntimeException("Cannot take the logarithm of zero");
+        }
+
+        return new ComplexNumber(Math.log(abs(num)), Math.atan2(num.IMAGINARY, num.REAL));
+    }
+
+    /**
+     * Computes the power of a complex number raised to another complex number.
+     *
+     * @param num1 the base complex number
+     * @param num2 the exponent complex number
+     * @return num1 raised to the power of num2
+     * link <a href="https://en.wikipedia.org/wiki/Exponentiation#Complex_exponents_with_a_positive_real_base">...</a>
+     */
+    public static ComplexNumber pow(ComplexNumber num1, ComplexNumber num2) {
+        if (num1.equals(ZERO)) {
+            return num2.equals(ZERO) ? ONE : ZERO;
+        }
+
+        return exp(multiply(ln(num1), num2));
+    }
+
+    /**
+     * Computes the square root of a complex number.
+     *
+     * @param num the complex number
+     * @return the square root of num
+     */
+    public static ComplexNumber sqrt(ComplexNumber num) {
+        return pow(num, new ComplexNumber(0.5, 0));
+    }
+
+    /**
+     * Computes the sine of a complex number.
+     *
+     * @param num the complex number
+     * @return the sine of num
+     * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_">...</a>(Euler's_formula)
+     */
+    public static ComplexNumber sin(ComplexNumber num) {
+        ComplexNumber exp1 = exp(multiply(num, PLUS_I));
+        ComplexNumber exp2 = exp(multiply(num, MINUS_I));
+        return divide(subtract(exp1, exp2), multiply(new ComplexNumber(2, 0), PLUS_I));
+    }
+
+    /**
+     * Computes the cosine of a complex number.
+     *
+     * @param num the complex number
+     * @return the cosine of num
+     * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Relationship_to_exponential_function_">...</a>(Euler's_formula)
+     */
+    public static ComplexNumber cos(ComplexNumber num) {
+        ComplexNumber exp1 = exp(multiply(num, PLUS_I));
+        ComplexNumber exp2 = exp(multiply(num, MINUS_I));
+        return divide(add(exp1, exp2), TWO);
+    }
+
+    /**
+     * Computes the tangent of a complex number.
+     *
+     * @param num the complex number
+     * @return the tangent of num
+     * @throws RuntimeException if <code>num.real = pi*(n+0.5)</code>
+     * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions">...</a>
+     */
+    public static ComplexNumber tan(ComplexNumber num) {
+        if (num.REAL % Math.PI == Math.PI / 2) {
+            throw new RuntimeException("Cannot take the tan of a number where the real part can be expressed as pi*(n+0.5)");
+        }
+
+        return divide(sin(num), cos(num));
+    }
+
+    /**
+     * Computes the cotangent of a complex number.
+     *
+     * @param num the complex number
+     * @return the cotangent of num
+     * @throws RuntimeException if <code>num.real = pi*n</code>
+     * @link <a href="https://en.wikipedia.org/wiki/Trigonometric_functions#Right-angled_triangle_definitions">...</a>
+     */
+    public static ComplexNumber cot(ComplexNumber num) {
+        if (num.REAL % Math.PI == 0) {
+            throw new RuntimeException("Cannot take the cot of number with real part dividable by pi");
+        }
+
+        return divide(cos(num), sin(num));
+    }
+
+    /**
+     * Computes the arcsine of a complex number.
+     *
+     * @param num the complex number
+     * @return the arcsine of num
+     * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a>
+     */
+    public static ComplexNumber arcsin(ComplexNumber num) {
+        ComplexNumber temp = sqrt(subtract(ONE, multiply(num, num)));
+        return multiply(MINUS_I, ln(add(multiply(PLUS_I, num), temp)));
+    }
+
+    /**
+     * Computes the arccosine of a complex number.
+     *
+     * @param num the complex number
+     * @return the arccosine of num
+     * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a>
+     */
+    public static ComplexNumber arccos(ComplexNumber num) {
+        ComplexNumber temp = sqrt(subtract(ONE, multiply(num, num)));
+        return multiply(MINUS_I, ln(add(num, multiply(temp, PLUS_I))));
+    }
+
+    /**
+     * Computes the arctangent of a complex number.
+     *
+     * @param num the complex number
+     * @return the arctangent of num
+     * @throws RuntimeException if <code>num=i</code> or <code>num=-i</code>
+     * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a>
+     */
+    public static ComplexNumber arctan(ComplexNumber num) {
+        if (num.equals(PLUS_I) || num.equals(MINUS_I)) {
+            throw new RuntimeException("Cannot take the arctan of " + num);
+        }
+
+        return multiply(divide(MINUS_I, TWO), ln(divide(subtract(PLUS_I, num), add(PLUS_I, num))));
+    }
+
+    /**
+     * Computes the arccotangent of a complex number.
+     *
+     * @param num the complex number
+     * @return the arccotangent of num
+     * @throws RuntimeException if <code>num=i</code> or <code>num=-i</code>
+     * @link <a href="https://en.wikipedia.org/wiki/Inverse_trigonometric_functions#Extension_to_the_complex_plane">...</a>
+     */
+    public static ComplexNumber arccot(ComplexNumber num) {
+        if (num.equals(PLUS_I) || num.equals(MINUS_I)) {
+            throw new RuntimeException("Cannot take the arccot of " + num);
+        }
+
+        return multiply(divide(MINUS_I, TWO), ln(divide(add(num, PLUS_I), subtract(num, PLUS_I))));
+    }
+}