Task: Quaternion type
Java: public class Quaternion {
    private final double a, b, c, d;

    public Quaternion(double a, double b, double c, double d) {
        this.a = a;
        this.b = b;
        this.c = c;
        this.d = d;
    }
    public Quaternion(double r) {
        this(r, 0.0, 0.0, 0.0);
    }

    public double norm() {
        return Math.sqrt(a * a + b * b + c * c + d * d);
    }

    public Quaternion negative() {
        return new Quaternion(-a, -b, -c, -d);
    }

    public Quaternion conjugate() {
        return new Quaternion(a, -b, -c, -d);
    }

    public Quaternion add(double r) {
        return new Quaternion(a + r, b, c, d);
    }
    public static Quaternion add(Quaternion q, double r) {
        return q.add(r);
    }
    public static Quaternion add(double r, Quaternion q) {
        return q.add(r);
    }
    public Quaternion add(Quaternion q) {
        return new Quaternion(a + q.a, b + q.b, c + q.c, d + q.d);
    }
    public static Quaternion add(Quaternion q1, Quaternion q2) {
        return q1.add(q2);
    }

    public Quaternion times(double r) {
        return new Quaternion(a * r, b * r, c * r, d * r);
    }
    public static Quaternion times(Quaternion q, double r) {
        return q.times(r);
    }
    public static Quaternion times(double r, Quaternion q) {
        return q.times(r);
    }
    public Quaternion times(Quaternion q) {
        return new Quaternion(
            a * q.a - b * q.b - c * q.c - d * q.d,
            a * q.b + b * q.a + c * q.d - d * q.c,
            a * q.c - b * q.d + c * q.a + d * q.b,
            a * q.d + b * q.c - c * q.b + d * q.a
        );
    }
    public static Quaternion times(Quaternion q1, Quaternion q2) {
        return q1.times(q2);
    }

    @Override
    public boolean equals(Object obj) {
        if (!(obj instanceof Quaternion)) return false;
        final Quaternion other = (Quaternion) obj;
        if (Double.doubleToLongBits(this.a) != Double.doubleToLongBits(other.a)) return false;
        if (Double.doubleToLongBits(this.b) != Double.doubleToLongBits(other.b)) return false;
        if (Double.doubleToLongBits(this.c) != Double.doubleToLongBits(other.c)) return false;
        if (Double.doubleToLongBits(this.d) != Double.doubleToLongBits(other.d)) return false;
        return true;
    }
    @Override
    public String toString() {
        return String.format("%.2f + %.2fi + %.2fj + %.2fk", a, b, c, d).replaceAll("\\+ -", "- ");
    }

    public String toQuadruple() {
        return String.format("(%.2f, %.2f, %.2f, %.2f)", a, b, c, d);
    }

    public static void main(String[] args) {
        Quaternion q = new Quaternion(1.0, 2.0, 3.0, 4.0);
        Quaternion q1 = new Quaternion(2.0, 3.0, 4.0, 5.0);
        Quaternion q2 = new Quaternion(3.0, 4.0, 5.0, 6.0);
        double r = 7.0;
        System.out.format("q       = %s%n", q);
        System.out.format("q1      = %s%n", q1);
        System.out.format("q2      = %s%n", q2);
        System.out.format("r       = %.2f%n%n", r);
        System.out.format("\u2016q\u2016     = %.2f%n", q.norm());
        System.out.format("-q      = %s%n", q.negative());
        System.out.format("q*      = %s%n", q.conjugate());
        System.out.format("q + r   = %s%n", q.add(r));
        System.out.format("q1 + q2 = %s%n", q1.add(q2));
        System.out.format("q \u00d7 r   = %s%n", q.times(r));
        Quaternion q1q2 = q1.times(q2);
        Quaternion q2q1 = q2.times(q1);
        System.out.format("q1 \u00d7 q2 = %s%n", q1q2);
        System.out.format("q2 \u00d7 q1 = %s%n", q2q1);
        System.out.format("q1 \u00d7 q2 %s q2 \u00d7 q1%n", (q1q2.equals(q2q1) ? "=" : "\u2260"));
    }
}

VB: Option Base 1
Private Function norm(q As Variant) As Double
    norm = Sqr(WorksheetFunction.SumSq(q))
End Function

Private Function negative(q) As Variant
    Dim res(4) As Double
    For i = 1 To 4
        res(i) = -q(i)
    Next i
    negative = res
End Function

Private Function conj(q As Variant) As Variant
    Dim res(4) As Double
    res(1) = q(1)
    For i = 2 To 4
        res(i) = -q(i)
    Next i
    conj = res
End Function

Private Function addr(r As Double, q As Variant) As Variant
    Dim res As Variant
    res = q
    res(1) = r + q(1)
    addr = res
End Function

Private Function add(q1 As Variant, q2 As Variant) As Variant
    add = WorksheetFunction.MMult(Array(1, 1), Array(q1, q2))
End Function

Private Function multr(r As Double, q As Variant) As Variant
    multr = WorksheetFunction.MMult(r, q)
End Function

Private Function mult(q1 As Variant, q2 As Variant)
    Dim res(4) As Double
    res(1) = q1(1) * q2(1) - q1(2) * q2(2) - q1(3) * q2(3) - q1(4) * q2(4)
    res(2) = q1(1) * q2(2) + q1(2) * q2(1) + q1(3) * q2(4) - q1(4) * q2(3)
    res(3) = q1(1) * q2(3) - q1(2) * q2(4) + q1(3) * q2(1) + q1(4) * q2(2)
    res(4) = q1(1) * q2(4) + q1(2) * q2(3) - q1(3) * q2(2) + q1(4) * q2(1)
    mult = res
End Function

Private Sub quats(q As Variant)
    Debug.Print q(1); IIf(q(2) < 0, " - " & Abs(q(2)), " + " & q(2));
    Debug.Print IIf(q(3) < 0, "i - " & Abs(q(3)), "i + " & q(3));
    Debug.Print IIf(q(4) < 0, "j - " & Abs(q(4)), "j + " & q(4)); "k"
End Sub

Public Sub quaternions()
    q = [{ 1, 2, 3, 4}]
    q1 = [{2, 3, 4, 5}]
    q2 = [{3, 4, 5, 6}]
    Dim r_ As Double
    r_ = 7#
    Debug.Print "q            = ";: quats q
    Debug.Print "q1           = ";: quats q1
    Debug.Print "q2           = ";: quats q2
    Debug.Print "r            = "; r_
    Debug.Print "norm(q)      = "; norm(q)
    Debug.Print "negative(q)  = ";: quats negative(q)
    Debug.Print "conjugate(q) = ";: quats conj(q)
    Debug.Print "r + q        = ";: quats addr(r_, q)
    Debug.Print "q1 + q2      = ";: quats add(q1, q2)
    Debug.Print "q * r        = ";: quats multr(r_, q)
    Debug.Print "q1 * q2      = ";: quats mult(q1, q2)
    Debug.Print "q2 * q1      = ";: quats mult(q2, q1)
End Sub