Powers Get Messy With Complex Numbers

Algebra Level 2

True or false :

\quad Let i = − 1 i = \sqrt{-1} , then − 1 = i 2 = i 4 / 2 = i 4 = 1 = 1 -1 = i^2 = i^{4/2} =\sqrt{i^4} = \sqrt1 = 1 .

True False

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Chung Kevin by Chung Kevin , 45, Australia

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2 solutions

The fourth root of 1 has many values.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Hung Woei Neoh
Apr 22, 2016

i 4 / 2 = i 4 i 2 ≠ i 4 i^{4/2} = \dfrac{i^4}{i^2} \neq \sqrt{i^4}

0 Helpful 0 Interesting 0 Brilliant 1 Confused

Hey....when you divide powers you don't divide by its bases, you substract their powers keeping the same base

Tanmoy Dutta - 3 years, 2 months ago

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