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A Number Raised to the m Power 
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#1
Feb214, 11:04 AM

P: 937

Hello Everyone,
I was wondering, does anyone know of a proof that showed if a number is raised to the mth power, where m is a positive even number, the number is always real? 


#3
Feb214, 11:17 AM

P: 937

Drats! I was hoping it was true! How about if m were only 2? Would the statement then be true?



#4
Feb214, 11:28 AM

P: 937

A Number Raised to the m Power
It isn't: (a + bi)(a + bi) = a^2 + 2abi + b^2i^2 = a^2 + 2abi  b^2



#5
Feb214, 11:28 AM

P: 445

Your claim will only be true for ##m=2## if the number is only real or imaginary. This is clear by expanding a complex number as a binomial. ##(a+bi)^2=a^2b^2+2abi## In order for this to be real, either ##a## or ##b## must be zero. You should check the case when ##m=4## by squaring ##(a^2b^2+abi)## to see what you get. Edit: I see that you figured it out as I was posting 


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