In R3, addition in the Wave Number system is straightforward. Opposite Values with Opposite Signs cancel each other out through interference. See the examples below:
Examples of R3 Addition
- 1^ + 0 = 1^; i^ + 0 = i^; j^ + 0 = j^
- 1^ + i^ + j^ = 1^ + i^ + j^
- 1v + 0 = 1v; iv + 0 = iv; jv + 0 = jv
- 1^ + 1v = 0; i^ + iv = 0; j^ + jv = 0
- 1v + 1^ = 0; iv + i^ = 0; jv + j^ = 0
- Addition is commutative
- 1v + iv + jv = 1v + iv + jv
- 0 + 0 = 0
- Note 0 is neither ^ or v
- 4^ + 6^ = 10^; 4i^ + 6i^ = 10i^; 4j^ + 6j^ = 10j^
- 4^ + 6^+ 3v = 7^; 4i^ + 6i^+ 3iv = 7i^; 4j^ + 6j^+ 3jv = 7j^
- 4v + 6^ + 3v = 1v; 4iv + 6i^ + 3iv = iv; 4jv + 6j^ + 3jv = jv
- (4v+ 6^) + 3v = 1v; (4iv+ 6i^) + 3iv = iv; (4jv+ 6j^) + 3jv = jv
- 4v+ (6^ + 3v) = 1v; 4iv+ (6i^ + 3iv) = iv; 4jv+ (6j^ + 3jv) = jv
- Addition is associative
- 4v + 6i^ + 3jv = 4v + 3jv+ 6i^ = 3jv + 4v + 6i^
- Order makes no difference
Conclusion
Try these examples of R3 addition with our online calculator.
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