Complex numbers - simple calculations

This example is tested with Xcode 9.2 playground in Swift 4.0.3. Basic complex number calculations such as the magnitude are includes as below:

class ComplexNum {

    var real : Float

    var imag : Float

    

    init (real: Float, imag: Float){

        self.real = real

        self.imag = imag

    }

    func show()->String {

        let plusChar = (imag>0) ? "+" : "-"

        return "\(real) \(plusChar) \(abs(imag))i"

    }

    //Magnitude

    func mag()->Float {

        return sqrt(self.real*self.real+self.imag*self.imag)

    }

    //Quick calculation with (i)

    func multiplyPlusI(num:ComplexNum) -> ComplexNum{

        return ComplexNum(real: -num.imag, imag: num.real)

    }

    //Quick calculation with (-i)

    func multiplyMinusI(num:ComplexNum) -> ComplexNum{

        return ComplexNum(real: num.imag, imag: -num.real)

    }

}

func addComplex(a: ComplexNum, b: ComplexNum)->ComplexNum {

    return ComplexNum(real: a.real+b.real, imag: a.imag+b.imag)

}

func multiplyComplex(a: ComplexNum, b: ComplexNum)->ComplexNum {

    return ComplexNum(real: a.real*b.real-a.imag*b.imag, imag: a.real*b.imag+a.imag*b.real)

}

let x = ComplexNum(real: 3, imag: 1)

print("x = \(x.show())")

print("|x| = \(x.mag())")

print("x(j) = \(x.multiplyPlusI(num: x).show())")

print("x(-j) = \(x.multiplyMinusI(num: x).show())")

let y = ComplexNum(real: -1, imag: -2)

print("y = \(y.show())")

print("|y| = \(y.mag())")

print("y(j) = \(x.multiplyPlusI(num: y).show())")

print("y(-j) = \(x.multiplyMinusI(num: y).show())")

print("x + y = \(addComplex(a: x, b: y).show())")
print("x * y = \(multiplyComplex(a: x, b: y).show())")

Results:

x = 3.0 + 1.0i

|x| = 3.16228

x(j) = -1.0 + 3.0i

x(-j) = 1.0 - 3.0i

y = -1.0 - 2.0i

|y| = 2.23607

y(j) = 2.0 - 1.0i

y(-j) = -2.0 + 1.0i

x + y = 2.0 - 1.0i

x * y = -1.0 - 7.0i

Related Information:
Matlab: Real and imaginary parts of complex number and multiplication with imaginary unit j