# B Imaginary number manipulations

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1. Apr 2, 2016

### Mr Davis 97

I know that this is probably a very commonly asked question with students, but say that we have $\sqrt{(-1)^2}$. If we performed the innermost operation first, then we have $\sqrt{(-1)^2} = \sqrt{1} = 1$. However, according to rules for radicals, we can do $\sqrt{(-1)^2} = (\sqrt{-1})^2 = -1$. Which one of these is the correct way of going about evaluating the expression, and why?

2. Apr 2, 2016

### Math_QED

$\sqrt{(a)^2}$ = |a|

3. Apr 2, 2016

### FactChecker

If you are really going to study imaginary and complex numbers, you will find out that roots do not have unique values, but rather they can have several "branches". Notice that (-1)2 = 1. So you could also have a square root, sqrt(), of 1 where sqrt( -12 ) = sqrt( 1) = -1. The standard definition of √ is that it is the "principle branch". But that is just a convention, not a mathematical rule.