Adding A Complex Number Class

Notes

• Class reference.
• Complex number operations.
• Basic Design
  • A complex number has two parts
    • A real part (a) , a float
    • An imaginary part (b) , a float
    • a + bi
    • $i = \sqrt{-1}$
  • We probably want getters and setters for these
    • constructor
    • Real() -> real part
    • Imag() -> returns imaginary part
    • toString() -> returns string a+bi
  • In addition, we will need a number of operations
    • add
    • subtract
    • multiply
    • divide
    • distance from 0 or magnitude
• Classes in javascript
  • No DEEP COPY
  • No operator overload
  • Only one constructor
  • Private member data names begin with a #
  • Members accessed via this.member
• Basic syntax:

  
  [export] class  ClassName {
      [optional field definitions]
  
      constructor() {
      }
  
      Member1() {
      }
      ...
  }
      

• Let's start this class.

• export class Complex {
      #real
      #imag
  
      constructor (a=0, b=0) {
         this.#real = a
         this.#imag = b
      }
  
      toString() {
         return this.#real + '+' + this.#imag + 'i'
      }
  } 

• In main.js import this import {complex} from "./complex.js"
• And test it

• function TestComplex() {
      let number = new Complex()
      console.log(number.toString())
  
      number = new Complex(1)
      console.log(number.toString())
  
      number = new Complex(3,2)
      console.log(number.toString())
  
  }
  
  ChangePicture(inset, canvas);
  TestComplex()  

• Implement add
  • a+bi + c+di = a+c + (b+d)i
  • We need to allocate a new complex for our return value
    • But Javascript does Garbage Collection so we don't have memory leaks.

  • Add(other){
        let rv = new Complex(this.#real, this.#imag)
        rv.#real += other.#real
        rv.#imag += other.#imag
        return rv
    }

• And add to TestComplex()

      let a = new Complex(3,4)
      let b = new Complex(5,9)
  
      let c = a.Add(b)
      console.log(a.toString() , " + ", b.toString(), " = ", c.toString())

• Complex subtraction : a+bi - c+di = a-c + (b-d)i
  • Implement and test this.
• a+bi * c+di = ac-bd + (ad+cb)i
  • implement and test this
• $\frac{a+bi}{c+di} = \frac {ac + bd} {c^2 + d^2} + \frac{bc - ad}{c^2 + d^2}$
  • implement and test this
• Magnitude or distance from 0 for a number is
  • $\sqrt{a^2 + b^2}$
  • Note, you will need Math.sqrt()
  • implement and test this