Question

Find all roots for z^2 + 2z + 1 = 0, where z is a complex number

Answer 1

The only thing I'm getting is obviously z=-1, but shouldn't there be another solution since this is of degree 2?

Answer 2

yeah it's a two degree,but both roots are -1, u are correct

Answer 3

I hope this is not a dumb question, but we saw a theorem that stated that any complex number has exactly n different n-th roots, so it makes me wonder how we get two identical roots :S?

Answer 4

or is this situation slightly different since we don't have the exact form z^n = some complex number? (again.. sorry if this is a stupid question)

Answer 5

sorry, i was busy, but this isn't a stupid question every complex equation of order n has n distinct roots you know a complex number z can be written as a+bi
a+bi is a root then a-bi is also a root
here in this case a=-1 and b=0
so this complex number is actually -1+0i, -1-0i
so here the roots are purely real which are same

Answer 6

thanks!