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If 1, `Omega` and `Omega^2` Are the Cube Roots of Unity, Prove `(A + B Omega + C Omega^2)/(C + S Omega + B Omega^2) = Omega^2` - ISC (Commerce) Class 12 - Mathematics

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Question

If 1, `omega` and `omega^2` are the cube roots of unity, prove `(a + b omega + c omega^2)/(c + s omega +  b omega^2) =  omega^2`

Solution

Taking LHS

`(a + b omega +  c omega^2)/(c + a omega +  b omega^2)`

`= (omega (a + b omega + c omega^2))/(omega(c + a omega + b omega^2))`

`= (a omega +  b omega^2 +  c omega^2)/(omega(c + a omega +  b omega^2) )= (a omega +  b omega^2 + c)/(omega(c + a omega + b omega^2))`

`= 1/omega xx omega^2/omega^2`

`=  omega^2`

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APPEARS IN

 2014-2015 (March) (with solutions)
Question 1.9 | 3.00 marks
Solution If 1, `Omega` and `Omega^2` Are the Cube Roots of Unity, Prove `(A + B Omega + C Omega^2)/(C + S Omega + B Omega^2) = Omega^2` Concept: Basic Concepts of Differential Equation.
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