Question

Find all z ∈ ℂ which satisfy z^2 + 2z + 1 = 0.

Answer 1

I need help with the working. I am sure if this is the correct way, but I reduced the equation to \[a ^{2} + 2a + 1 +(2a + bi + 2)bi = 0\]

Answer 2

i am not sure

Answer 3

but from there i'm not sure how to proceed

Answer 4

instead of putting z=a+bi, you just find first the value of z
equation is z^2+z+1=0
so (z+1)^2=0
z=-1
so z is purely real
if we write in terms of a+bi then here it's -1+0i
the other root is -1-0i
so both the roots are same here,and purely real

Answer 5

Thx! :)

Answer 6

glad to help