A Number Raised to the m Power


by Bashyboy
Tags: number, power, raised
Bashyboy
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#1
Feb2-14, 11:04 AM
P: 878
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?
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Borek
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#2
Feb2-14, 11:07 AM
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(1+2i)4 = -7-24i
Bashyboy
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#3
Feb2-14, 11:17 AM
P: 878
Drats! I was hoping it was true! How about if m were only 2? Would the statement then be true?

Bashyboy
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#4
Feb2-14, 11:28 AM
P: 878

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
DrewD
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#5
Feb2-14, 11:28 AM
P: 427
Quote Quote by Bashyboy View Post
Drats! I was hoping it was true! How about if m were only 2? Would the statement then be true?
##(1+i)^2=1+2i-1=2i##

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^2-b^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^2-b^2+abi)## to see what you get.


Edit: I see that you figured it out as I was posting


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