Task: Imaginary base numbers
C#: using System;
using System.Linq;
using System.Text;

namespace ImaginaryBaseNumbers {
    class Complex {
        private double real, imag;

        public Complex(int r, int i) {
            real = r;
            imag = i;
        }

        public Complex(double r, double i) {
            real = r;
            imag = i;
        }

        public static Complex operator -(Complex self) =>
            new Complex(-self.real, -self.imag);

        public static Complex operator +(Complex rhs, Complex lhs) =>
            new Complex(rhs.real + lhs.real, rhs.imag + lhs.imag);

        public static Complex operator -(Complex rhs, Complex lhs) =>
            new Complex(rhs.real - lhs.real, rhs.imag - lhs.imag);

        public static Complex operator *(Complex rhs, Complex lhs) =>
            new Complex(
                rhs.real * lhs.real - rhs.imag * lhs.imag,
                rhs.real * lhs.imag + rhs.imag * lhs.real
                );

        public static Complex operator *(Complex rhs, double lhs) =>
             new Complex(rhs.real * lhs, rhs.imag * lhs);

        public static Complex operator /(Complex rhs, Complex lhs) =>
            rhs * lhs.Inv();

        public Complex Inv() {
            double denom = real * real + imag * imag;
            return new Complex(real / denom, -imag / denom);
        }

        public QuaterImaginary ToQuaterImaginary() {
            if (real == 0.0 && imag == 0.0) return new QuaterImaginary("0");
            int re = (int)real;
            int im = (int)imag;
            int fi = -1;
            StringBuilder sb = new StringBuilder();
            while (re != 0) {
                int rem = re % -4;
                re /= -4;
                if (rem < 0) {
                    rem = 4 + rem;
                    re++;
                }
                sb.Append(rem);
                sb.Append(0);
            }
            if (im != 0) {
                double f = (new Complex(0.0, imag) / new Complex(0.0, 2.0)).real;
                im = (int)Math.Ceiling(f);
                f = -4.0 * (f - im);
                int index = 1;
                while (im != 0) {
                    int rem = im % -4;
                    im /= -4;
                    if (rem < 0) {
                        rem = 4 + rem;
                        im++;
                    }
                    if (index < sb.Length) {
                        sb[index] = (char)(rem + 48);
                    } else {
                        sb.Append(0);
                        sb.Append(rem);
                    }
                    index += 2;
                }
                fi = (int)f;
            }
            string reverse = new string(sb.ToString().Reverse().ToArray());
            sb.Length = 0;
            sb.Append(reverse);
            if (fi != -1) sb.AppendFormat(".{0}", fi);
            string s = sb.ToString().TrimStart('0');
            if (s[0] == '.') s = "0" + s;
            return new QuaterImaginary(s);
        }

        public override string ToString() {
            double real2 = (real == -0.0) ? 0.0 : real;  
            double imag2 = (imag == -0.0) ? 0.0 : imag;  
            if (imag2 == 0.0) {
                return string.Format("{0}", real2);
            }
            if (real2 == 0.0) {
                return string.Format("{0}i", imag2);
            }
            if (imag2 > 0.0) {
                return string.Format("{0} + {1}i", real2, imag2);
            }
            return string.Format("{0} - {1}i", real2, -imag2);
        }
    }

    class QuaterImaginary {
        internal static Complex twoI = new Complex(0.0, 2.0);
        internal static Complex invTwoI = twoI.Inv();

        private string b2i;

        public QuaterImaginary(string b2i) {
            if (b2i == "" || !b2i.All(c => "0123.".IndexOf(c) > -1) || b2i.Count(c => c == '.') > 1) {
                throw new Exception("Invalid Base 2i number");
            }
            this.b2i = b2i;
        }

        public Complex ToComplex() {
            int pointPos = b2i.IndexOf(".");
            int posLen = (pointPos != -1) ? pointPos : b2i.Length;
            Complex sum = new Complex(0.0, 0.0);
            Complex prod = new Complex(1.0, 0.0);
            for (int j = 0; j < posLen; j++) {
                double k = (b2i[posLen - 1 - j] - '0');
                if (k > 0.0) {
                    sum += prod * k;
                }
                prod *= twoI;
            }
            if (pointPos != -1) {
                prod = invTwoI;
                for (int j = posLen + 1; j < b2i.Length; j++) {
                    double k = (b2i[j] - '0');
                    if (k > 0.0) {
                        sum += prod * k;
                    }
                    prod *= invTwoI;
                }
            }

            return sum;
        }

        public override string ToString() {
            return b2i;
        }
    }

    class Program {
        static void Main(string[] args) {
            for (int i = 1; i <= 16; i++) {
                Complex c1 = new Complex(i, 0);
                QuaterImaginary qi = c1.ToQuaterImaginary();
                Complex c2 = qi.ToComplex();
                Console.Write("{0,4} -> {1,8} -> {2,4}     ", c1, qi, c2);
                c1 = -c1;
                qi = c1.ToQuaterImaginary();
                c2 = qi.ToComplex();
                Console.WriteLine("{0,4} -> {1,8} -> {2,4}", c1, qi, c2);
            }
            Console.WriteLine();
            for (int i = 1; i <= 16; i++) {
                Complex c1 = new Complex(0, i);
                QuaterImaginary qi = c1.ToQuaterImaginary();
                Complex c2 = qi.ToComplex();
                Console.Write("{0,4} -> {1,8} -> {2,4}     ", c1, qi, c2);
                c1 = -c1;
                qi = c1.ToQuaterImaginary();
                c2 = qi.ToComplex();
                Console.WriteLine("{0,4} -> {1,8} -> {2,4}", c1, qi, c2);
            }
        }
    }
}

Go: package main

import (
    "fmt"
    "math"
    "strconv"
    "strings"
)

const (
    twoI    = 2.0i
    invTwoI = 1.0 / twoI
)

type quaterImaginary struct {
    b2i string
}

func reverse(s string) string {
    r := []rune(s)
    for i, j := 0, len(r)-1; i < len(r)/2; i, j = i+1, j-1 {
        r[i], r[j] = r[j], r[i]
    }
    return string(r)
}

func newQuaterImaginary(b2i string) quaterImaginary {
    b2i = strings.TrimSpace(b2i)
    _, err := strconv.ParseFloat(b2i, 64)
    if err != nil {
        panic("invalid Base 2i number")
    }
    return quaterImaginary{b2i}
}

func toComplex(q quaterImaginary) complex128 {
    pointPos := strings.Index(q.b2i, ".")
    var posLen int
    if pointPos != -1 {
        posLen = pointPos
    } else {
        posLen = len(q.b2i)
    }
    sum := 0.0i
    prod := complex(1.0, 0.0)
    for j := 0; j < posLen; j++ {
        k := float64(q.b2i[posLen-1-j] - '0')
        if k > 0.0 {
            sum += prod * complex(k, 0.0)
        }
        prod *= twoI
    }
    if pointPos != -1 {
        prod = invTwoI
        for j := posLen + 1; j < len(q.b2i); j++ {
            k := float64(q.b2i[j] - '0')
            if k > 0.0 {
                sum += prod * complex(k, 0.0)
            }
            prod *= invTwoI
        }
    }
    return sum
}

func (q quaterImaginary) String() string {
    return q.b2i
}


func toQuaterImaginary(c complex128) quaterImaginary {
    if c == 0i {
        return quaterImaginary{"0"}
    }
    re := int(real(c))
    im := int(imag(c))
    fi := -1
    var sb strings.Builder
    for re != 0 {
        rem := re % -4
        re /= -4
        if rem < 0 {
            rem += 4
            re++
        }
        sb.WriteString(strconv.Itoa(rem))
        sb.WriteString("0")
    }
    if im != 0 {
        f := real(complex(0.0, imag(c)) / 2.0i)
        im = int(math.Ceil(f))
        f = -4.0 * (f - float64(im))
        index := 1
        for im != 0 {
            rem := im % -4
            im /= -4
            if rem < 0 {
                rem += 4
                im++
            }
            if index < sb.Len() {
                bs := []byte(sb.String())
                bs[index] = byte(rem + 48)
                sb.Reset()
                sb.Write(bs)
            } else {
                sb.WriteString("0")
                sb.WriteString(strconv.Itoa(rem))
            }
            index += 2
        }
        fi = int(f)
    }
    s := reverse(sb.String())
    if fi != -1 {
        s = fmt.Sprintf("%s.%d", s, fi)
    }
    s = strings.TrimLeft(s, "0")
    if s[0] == '.' {
        s = "0" + s
    }
    return newQuaterImaginary(s)
}

func main() {
    for i := 1; i <= 16; i++ {
        c1 := complex(float64(i), 0.0)
        qi := toQuaterImaginary(c1)
        c2 := toComplex(qi)
        fmt.Printf("%4.0f -> %8s -> %4.0f     ", real(c1), qi, real(c2))
        c1 = -c1
        qi = toQuaterImaginary(c1)
        c2 = toComplex(qi)
        fmt.Printf("%4.0f -> %8s -> %4.0f\n", real(c1), qi, real(c2))
    }
    fmt.Println()
    for i := 1; i <= 16; i++ {
        c1 := complex(0.0, float64(i))
        qi := toQuaterImaginary(c1)
        c2 := toComplex(qi)
        fmt.Printf("%3.0fi -> %8s -> %3.0fi     ", imag(c1), qi, imag(c2))
        c1 = -c1
        qi = toQuaterImaginary(c1)
        c2 = toComplex(qi)
        fmt.Printf("%3.0fi -> %8s -> %3.0fi\n", imag(c1), qi, imag(c2))
    }
}