import kotlin.math.pow
import kotlin.math.sqrt


data class Complex(val re: Double, val im: Double) {

    companion object {
        val zero = Complex(0.0, 0.0)
    }

    fun reciprocal(): Complex {
        val scale = re.pow(2) + re.pow(2)
        return Complex(re / scale, -im / scale)
    }

    fun inCardioid(): Boolean {
        val pq = (re - 0.25).pow(2) + im.pow(2)
        return re < sqrt(pq) - (2*pq) + 0.25
    }

    fun dsq(): Double = re*re + im*im

    fun abs(): Double = sqrt(re.pow(2) + im.pow(2))

    operator fun unaryMinus(): Complex = Complex(-re, -im)
    operator fun plus(other: Double): Complex = Complex(re + other, im)
    operator fun minus(other: Double): Complex = Complex(re - other, im)
    operator fun times(other: Double): Complex = Complex(re * other, im * other)
    operator fun div(other: Double): Complex = Complex(re / other, im / other)

    operator fun plus(other: Complex): Complex =
        Complex(re + other.re, im + other.im)

    operator fun minus(other: Complex): Complex =
        Complex(re - other.re, im - other.im)

    operator fun times(other: Complex): Complex =
        Complex(
            (re * other.re) - (im * other.im),
            (re * other.im) + (im * other.re))

    operator fun div(other: Complex): Complex = this * other.reciprocal()

    //@Override
    //fun equals(other: Complex): Boolean = this.im == other.im && this.re == other.re

}