From e252eb631db97ed5c4ca8d082072aaf77c0c7657 Mon Sep 17 00:00:00 2001
From: Oleksii Trekhleb <trehleb@gmail.com>
Date: Tue, 14 Aug 2018 22:56:13 +0300
Subject: [PATCH] Add polar representation of complex numbers.

---
 .../math/complex-number/ComplexNumber.js      | 45 +++++++++++++++++++
 .../__test__/ComplexNumber.test.js            | 27 +++++++++++
 2 files changed, 72 insertions(+)

diff --git a/src/algorithms/math/complex-number/ComplexNumber.js b/src/algorithms/math/complex-number/ComplexNumber.js
index 5f33e071..801c0c37 100644
--- a/src/algorithms/math/complex-number/ComplexNumber.js
+++ b/src/algorithms/math/complex-number/ComplexNumber.js
@@ -1,5 +1,10 @@
+import radianToDegree from '../radian/radianToDegree';
+
 export default class ComplexNumber {
   /**
+   * z = re + im * i
+   * z = radius * e^(i * phase)
+   *
    * @param {number} [re]
    * @param {number} [im]
    */
@@ -70,4 +75,44 @@ export default class ComplexNumber {
       im: -1 * complexNumber.im,
     });
   }
+
+  /**
+   * @return {number}
+   */
+  getRadius() {
+    return Math.sqrt((this.re ** 2) + (this.im ** 2));
+  }
+
+  /**
+   * @param {boolean} [inRadians]
+   * @return {number}
+   */
+  getPhase(inRadians = true) {
+    let phase = Math.atan(Math.abs(this.im) / Math.abs(this.re));
+
+    if (this.re < 0 && this.im > 0) {
+      phase = Math.PI - phase;
+    } else if (this.re < 0 && this.im < 0) {
+      phase = -(Math.PI - phase);
+    } else if (this.re > 0 && this.im < 0) {
+      phase = -phase;
+    }
+
+    if (!inRadians) {
+      phase = radianToDegree(phase);
+    }
+
+    return phase;
+  }
+
+  /**
+   * @param {boolean} [inRadians]
+   * @return {{radius: number, phase: number}}
+   */
+  getPolarForm(inRadians = true) {
+    return {
+      radius: this.getRadius(),
+      phase: this.getPhase(inRadians),
+    };
+  }
 }
diff --git a/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js b/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js
index a25b93e0..827d2308 100644
--- a/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js
+++ b/src/algorithms/math/complex-number/__test__/ComplexNumber.test.js
@@ -110,4 +110,31 @@ describe('ComplexNumber', () => {
     expect(complexNumber3.re).toBe(-7 / 41);
     expect(complexNumber3.im).toBe(22 / 41);
   });
+
+  it('should return complex number in polar form', () => {
+    const complexNumber1 = new ComplexNumber({ re: 3, im: 3 });
+    expect(complexNumber1.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2)));
+    expect(complexNumber1.getPolarForm().phase).toBe(Math.PI / 4);
+    expect(complexNumber1.getPolarForm(false).phase).toBe(45);
+
+    const complexNumber2 = new ComplexNumber({ re: -3, im: 3 });
+    expect(complexNumber2.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2)));
+    expect(complexNumber2.getPolarForm().phase).toBe(3 * (Math.PI / 4));
+    expect(complexNumber2.getPolarForm(false).phase).toBe(135);
+
+    const complexNumber3 = new ComplexNumber({ re: -3, im: -3 });
+    expect(complexNumber3.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2)));
+    expect(complexNumber3.getPolarForm().phase).toBe(-3 * (Math.PI / 4));
+    expect(complexNumber3.getPolarForm(false).phase).toBe(-135);
+
+    const complexNumber4 = new ComplexNumber({ re: 3, im: -3 });
+    expect(complexNumber4.getPolarForm().radius).toBe(Math.sqrt((3 ** 2) + (3 ** 2)));
+    expect(complexNumber4.getPolarForm().phase).toBe(-1 * (Math.PI / 4));
+    expect(complexNumber4.getPolarForm(false).phase).toBe(-45);
+
+    const complexNumber5 = new ComplexNumber({ re: 5, im: 7 });
+    expect(complexNumber5.getPolarForm().radius).toBeCloseTo(8.60);
+    expect(complexNumber5.getPolarForm().phase).toBeCloseTo(0.95);
+    expect(complexNumber5.getPolarForm(false).phase).toBeCloseTo(54.46);
+  });
 });