R2 – Multiplication – Dot Product

Dot product multiplication in R2 uses the same approach as in classical maths by using the formula:

Dot product of a.b = (ax*bx) + (ay*by) where ax, bx, ay and by are the Counters of the Opposite Values a and b. For example:

• (3^{^} + 2i^{^}).(1^{^} + 4i^{^}) = 3*1 + 2*4 = 11. Here (3^{^} + 2i^{^}) is the operator, . is the operation and (1^{^} + 4i^{^}) is the operand.

The dot product is based on the Counters of the Opposite Values with ^v Opposite Signs represented as a flip.

Example R2 Dot Products

• 1^v. 2^{^} = ^–1*2 = ^–2
• 2i^v. 4i^v  = ^–2*^–4= 8
• (3^{^} + 2i^{^}).(1^{^} + 4i^{^}) = 3*1 + 2*4 = 11
• (3^{^} + 2i^{^}).(1^{^} + 4i^v) = 3*1 + 2*^–4 = ^–5
• (3^v + 2i^{^}).(1^{^} + 4i^{^}) = ^–3*1 + 2*4 = 5
• (6^{^} + 5i^v).(4^v + 3i^{^}) = 6*^–4 + ^–5*4 = ^–39

Conclusion

Try these examples of R2 dot product multiplication with our online calculator.

Finally, the output of the dot product is a Counter and can only be used as such.

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