R3 – Addition

In R3, addition in the Wave Number system is straightforward. Opposite Values with Opposite Signs cancel each other out. See the examples below:

Examples of R3 Addition

• 1^{^} + 0 = 1^{^}; i^{^} + 0 = i^{^};   j^{^} + 0 = j^{^}
• 1^{^} + i^{^} + j^{^} =  1^{^} + i^{^} + j^{^}
• 1^v + 0 = 1^v; i^v + 0 = i^v;   j^v + 0 = j^v           
• 1^{^} + 1^v  = 0; i^{^} + i^v = 0;  j^{^} + j^v = 0            
• 1^v + 1^{^}  = 0;  i^v + i^{^}  = 0;  j^v + j^{^}  = 0 
  • Addition is commutative

• 1^v + i^v + j^v = 1^v + i^v + j^v
• 0 + 0 = 0           
  • Note 0 is neither ^{^} or ^v

• 4^{^} + 6^{^}  = 10^{^}; 4i^{^} + 6i^{^} = 10i^{^};  4j^{^} + 6j^{^} = 10j^{^}
• 4^{^} + 6^{^}+ 3^v = 7^{^}; 4i^{^} + 6i^{^}+ 3i^v = 7i^{^};  4j^{^} + 6j^{^}+ 3j^v = 7j^{^}
• 4^v + 6^{^} + 3^v  = 1^v; 4i^v + 6i^{^} + 3i^v  = i^v;    4j^v + 6j^{^} + 3j^v  = j^v
• (4^v+ 6^{^}) + 3^v = 1^v; (4i^v+ 6i^{^}) + 3i^v = i^v;  (4j^v+ 6j^{^}) + 3j^v = j^v
• 4^v+ (6^{^} + 3^v) = 1^v; 4i^v+ (6i^{^} + 3i^v) = i^v; 4j^v+ (6j^{^} + 3j^v) = j^v  
  • Addition is associative

• 4^v + 6i^{^} + 3j^v  = 4^v + 3j^v+ 6i^{^}  = 3j^v + 4^v + 6i^{^}
  • Order makes no difference

Conclusion

Try these examples of R3 addition with our online calculator.

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