Complex Style

Algebra Level 2

( a b ) c = a b c (a^b)^c=a^{bc} Is this true for complex numbers?

Yes No

X X by X X , 17, Taiwan

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1 solution

One counterexample is: ( ( − 1 ) 2 ) 0.5 ((-1)^2)^{0.5} = 1 0.5 = 1 1^{0.5}=1 , but ( − 1 ) 2 × 0.5 = − 1 (-1)^{2\times0.5}=-1 .

So the above property isn't true even for real numbers, so it would also not be true for complex.

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