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Question: Solving algebraic equations with complex unknowns

Sorry if this is a well-known feature of Maple, but I haven't had much success searching for an answer.

Consider trying to separately solve each of the following two equations for x.

 

alpha * x + conjugate(alpha) * x = 1 

Maple 15 solves this equation to give x = 1/(alpha + conjugate(alpha)) , as expected.

 

alpha * x - conjugate(alpha) * x = 1

Maple 15 fails to solve this equation, returning nothing as if there is no solution.

 

I thought all variables were viewed as complex, so I don't understand why Maple treats these equations so differently.

How do I get Maple to solve the second equation?

 

Thanks for any advice.

Charlie

 

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