Fix bug with converting complex number into polar form.

Author: trekhleb

src/algorithms/math/complex-number/ComplexNumber.js

@@ -14,51 +14,63 @@ export default class ComplexNumber {
   }
 
   /**
-   * @param {ComplexNumber} addend
+   * @param {ComplexNumber|number} addend
    * @return {ComplexNumber}
    */
   add(addend) {
+    // Make sure we're dealing with complex number.
+    const complexAddend = this.toComplexNumber(addend);
+
     return new ComplexNumber({
-      re: this.re + addend.re,
-      im: this.im + addend.im,
+      re: this.re + complexAddend.re,
+      im: this.im + complexAddend.im,
     });
   }
 
   /**
-   * @param {ComplexNumber} subtrahend
+   * @param {ComplexNumber|number} subtrahend
    * @return {ComplexNumber}
    */
   subtract(subtrahend) {
+    // Make sure we're dealing with complex number.
+    const complexSubtrahend = this.toComplexNumber(subtrahend);
+
     return new ComplexNumber({
-      re: this.re - subtrahend.re,
-      im: this.im - subtrahend.im,
+      re: this.re - complexSubtrahend.re,
+      im: this.im - complexSubtrahend.im,
     });
   }
 
   /**
-   * @param {ComplexNumber} multiplicand
+   * @param {ComplexNumber|number} multiplicand
    * @return {ComplexNumber}
    */
   multiply(multiplicand) {
+    // Make sure we're dealing with complex number.
+    const complexMultiplicand = this.toComplexNumber(multiplicand);
+
     return new ComplexNumber({
-      re: this.re * multiplicand.re - this.im * multiplicand.im,
-      im: this.re * multiplicand.im + this.im * multiplicand.re,
+      re: this.re * complexMultiplicand.re - this.im * complexMultiplicand.im,
+      im: this.re * complexMultiplicand.im + this.im * complexMultiplicand.re,
     });
   }
 
   /**
-   * @param {ComplexNumber} divider
+   * @param {ComplexNumber|number} divider
    * @return {ComplexNumber}
    */
   divide(divider) {
+    // Make sure we're dealing with complex number.
+    const complexDivider = this.toComplexNumber(divider);
+
     // Get divider conjugate.
-    const dividerConjugate = this.conjugate(divider);
+    const dividerConjugate = this.conjugate(complexDivider);
 
     // Multiply dividend by divider's conjugate.
     const finalDivident = this.multiply(dividerConjugate);
 
     // Calculating final divider using formula (a + bi)(a − bi) = a^2 + b^2
-    const finalDivider = (divider.re ** 2) + (divider.im ** 2);
+    const finalDivider = (complexDivider.re ** 2) + (complexDivider.im ** 2);
 
     return new ComplexNumber({
       re: finalDivident.re / finalDivider,
@@ -67,9 +79,12 @@ export default class ComplexNumber {
   }
 
   /**
-   * @param {ComplexNumber} complexNumber
+   * @param {ComplexNumber|number} number
    */
-  conjugate(complexNumber) {
+  conjugate(number) {
+    // Make sure we're dealing with complex number.
+    const complexNumber = this.toComplexNumber(number);
+
     return new ComplexNumber({
       re: complexNumber.re,
       im: -1 * complexNumber.im,
@@ -96,6 +111,18 @@ export default class ComplexNumber {
       phase = -(Math.PI - phase);
     } else if (this.re > 0 && this.im < 0) {
       phase = -phase;
+    } else if (this.re === 0 && this.im > 0) {
+      phase = Math.PI / 2;
+    } else if (this.re === 0 && this.im < 0) {
+      phase = -Math.PI / 2;
+    } else if (this.re < 0 && this.im === 0) {
+      phase = Math.PI;
+    } else if (this.re > 0 && this.im === 0) {
+      phase = 0;
+    } else if (this.re === 0 && this.im === 0) {
+      // More correctly would be to set 'indeterminate'.
+      // But just for simplicity reasons let's set zero.
+      phase = 0;
     }
 
     if (!inRadians) {
@@ -115,4 +142,19 @@ export default class ComplexNumber {
       phase: this.getPhase(inRadians),
     };
   }
+
+  /**
+   * Convert real numbers to complex number.
+   * In case if complex number is provided then lefts it as is.
+   *
+   * @param {ComplexNumber|number} number
+   * @return {ComplexNumber}
+   */
+  toComplexNumber(number) {
+    if (number instanceof ComplexNumber) {
+      return number;
+    }
+
+    return new ComplexNumber({ re: number });
+  }
 }

src/algorithms/math/complex-number/__test__/ComplexNumber.test.js

@@ -33,12 +33,16 @@ describe('ComplexNumber', () => {
 
     const complexNumber3 = complexNumber.add(realNumber);
     const complexNumber4 = realNumber.add(complexNumber);
+    const complexNumber5 = complexNumber.add(3);
 
     expect(complexNumber3.re).toBe(1 + 3);
     expect(complexNumber3.im).toBe(2);
 
     expect(complexNumber4.re).toBe(1 + 3);
     expect(complexNumber4.im).toBe(2);
+
+    expect(complexNumber5.re).toBe(1 + 3);
+    expect(complexNumber5.im).toBe(2);
   });
 
   it('should subtract complex numbers', () => {
@@ -61,12 +65,16 @@ describe('ComplexNumber', () => {
 
     const complexNumber3 = complexNumber.subtract(realNumber);
     const complexNumber4 = realNumber.subtract(complexNumber);
+    const complexNumber5 = complexNumber.subtract(3);
 
     expect(complexNumber3.re).toBe(1 - 3);
     expect(complexNumber3.im).toBe(2);
 
     expect(complexNumber4.re).toBe(3 - 1);
     expect(complexNumber4.im).toBe(-2);
+
+    expect(complexNumber5.re).toBe(1 - 3);
+    expect(complexNumber5.im).toBe(2);
   });
 
   it('should multiply complex numbers', () => {
@@ -75,12 +83,16 @@ describe('ComplexNumber', () => {
 
     const complexNumber3 = complexNumber1.multiply(complexNumber2);
     const complexNumber4 = complexNumber2.multiply(complexNumber1);
+    const complexNumber5 = complexNumber1.multiply(5);
 
     expect(complexNumber3.re).toBe(-11);
     expect(complexNumber3.im).toBe(23);
 
     expect(complexNumber4.re).toBe(-11);
     expect(complexNumber4.im).toBe(23);
+
+    expect(complexNumber5.re).toBe(15);
+    expect(complexNumber5.im).toBe(10);
   });
 
   it('should multiply complex numbers by themselves', () => {
@@ -106,9 +118,13 @@ describe('ComplexNumber', () => {
     const complexNumber2 = new ComplexNumber({ re: 4, im: -5 });
 
     const complexNumber3 = complexNumber1.divide(complexNumber2);
+    const complexNumber4 = complexNumber1.divide(2);
 
     expect(complexNumber3.re).toBe(-7 / 41);
     expect(complexNumber3.im).toBe(22 / 41);
+
+    expect(complexNumber4.re).toBe(1);
+    expect(complexNumber4.im).toBe(1.5);
   });
 
   it('should return complex number in polar form', () => {
@@ -136,5 +152,30 @@ describe('ComplexNumber', () => {
     expect(complexNumber5.getPolarForm().radius).toBeCloseTo(8.60);
     expect(complexNumber5.getPolarForm().phase).toBeCloseTo(0.95);
     expect(complexNumber5.getPolarForm(false).phase).toBeCloseTo(54.46);
+
+    const complexNumber6 = new ComplexNumber({ re: 0, im: 0.25 });
+    expect(complexNumber6.getPolarForm().radius).toBeCloseTo(0.25);
+    expect(complexNumber6.getPolarForm().phase).toBeCloseTo(1.57);
+    expect(complexNumber6.getPolarForm(false).phase).toBeCloseTo(90);
+
+    const complexNumber7 = new ComplexNumber({ re: 0, im: -0.25 });
+    expect(complexNumber7.getPolarForm().radius).toBeCloseTo(0.25);
+    expect(complexNumber7.getPolarForm().phase).toBeCloseTo(-1.57);
+    expect(complexNumber7.getPolarForm(false).phase).toBeCloseTo(-90);
+
+    const complexNumber8 = new ComplexNumber();
+    expect(complexNumber8.getPolarForm().radius).toBeCloseTo(0);
+    expect(complexNumber8.getPolarForm().phase).toBeCloseTo(0);
+    expect(complexNumber8.getPolarForm(false).phase).toBeCloseTo(0);
+
+    const complexNumber9 = new ComplexNumber({ re: -0.25, im: 0 });
+    expect(complexNumber9.getPolarForm().radius).toBeCloseTo(0.25);
+    expect(complexNumber9.getPolarForm().phase).toBeCloseTo(Math.PI);
+    expect(complexNumber9.getPolarForm(false).phase).toBeCloseTo(180);
+
+    const complexNumber10 = new ComplexNumber({ re: 0.25, im: 0 });
+    expect(complexNumber10.getPolarForm().radius).toBeCloseTo(0.25);
+    expect(complexNumber10.getPolarForm().phase).toBeCloseTo(0);
+    expect(complexNumber10.getPolarForm(false).phase).toBeCloseTo(0);
   });
 });