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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

ConceptBasic Concepts of Differential Equation

#### 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

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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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