R2 – Division – Flipping

Flipping in R2 division can be applied to the individual Opposite Values or to the result to reverse their signs.

R2 Division Table

Flipping Opposite Values in R2

• ^–6^v/3i^v = 6^{^}/3i^v = 2i^{^}
• 6^v/^–3i^v = 6^v/3i^{^} = 2i^{^}                       
• 1^{^}*(^–i^{^}/^–1^{^}) = 1^{^}*(i^v/1^v)   = 1^{^}*i^{^}  = i^{^} 
  • Note that 2 flips cancel out i^{^}/1^{^} = i^{^}, i^v/1^v = i^{^}

• 1^v*(^–1^{^}/^–i^{^})  = 1^v*(1^v/i^v)   1^v*i^v  = i^{^}
• 3^{^}*(^–4i^{^}/3^v)  = 3^{^}*(4i^v/3^v) = 3^{^}*(4i^{^}/3)  = 4i^{^}
• (3^{^}*^–4i^{^})/3^v = (3^{^}*4i^v)/3^v =12i^v/3^v = 4i^{^}
  • Note that multiplication part of the equation is associative

• 3^{^}*(^–4i^v/^–3) = 3^{^}*(4i^v/3) =  (3^{^}*4i^v)/3 =  12i^v/3 =   4i^v
• 3i^{^}*(^–4^v/^–3i^{^})= 3i^{^}*(4^{^}/3i^v)= 3i^{^}*(4i^{^}/3)= 12^v/3= 4^v       
  • Note that the flip on the divisor cancels out the flip on the numerator. i.e. 4^v/3i^{^} = 4i^{^}/3 = 4^{^}/3i^v

Flipping Counters in R2

The flip sign applies to the result when used with a Counter. This is because Counters do not have an Opposite Sign to flip. For example:

• 6i^v/^–3 = 2i^{^}

The flip on the Counter divisor cancels out the flip on the Opposite Value numerator. For example:

• 3^{^}*(^–4i^v/^–3) = 3^{^}*(4i^{^}/^–3) = 3^{^}*(4i^v/3) = 12i^v/3 = 4i^v

Flipping Terms

The Opposite Value of a term must be worked out before the flipping can take place. An exception to this is where 2 flips happen together and cancel each other out. For example:

• b*(^–a/^–b) = a
• ^–2*^–2a = 4a

Conclusion

Try these examples of flipping and R2 division with our online calculator.

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