Question

Is the nth root of a negative number positive or negative?

Answer 1

For example \[\sqrt[4]{-81}\]
Is one of the answers \[3i(\cos(\pi/4)+isin(\pi/4))\] or just \[3(\cos(\pi/4)+isin(\pi/4))\]

Answer 2

The second one.

Answer 3

why?

Answer 4

Because that is the polar form of a complex number. And an even root of a negative number is complex.