Question

How is it wrong?
\[\large 1 = \sqrt{1} = \sqrt{i^4} = i^2 = -1\]

Answer 1

The product property of square roots applies only to positive, real numbers.

Answer 2

I guess it's because \(i^4 = (i^2)^2\), so we have \(\sqrt{(-1)^2}\neq\sqrt{-1}\sqrt{-1}\).

Am I correct?

Answer 3

no directrix is always right....

Answer 4

So I am wrong? @acxbox22

Answer 5

We basically said the same thing lol...

Answer 6

well @Directrix stated a rue of exponents
because you can only use exponent rules with real numbers
i is imaginary and hence is not real