Question

Find all z ∈ ℂ which satisfy z^2 + 2(conjugate of z) + 1 = 0

Answer 1

I tried replacing z with a+bi, and reduced the equation to \[a ^{2}+2a+1 + (2a +bi -2) bi=0\]

Answer 2

that's what i was gonna tell you

Answer 3

then set the real part = 0, and the imaginary part = 0

Answer 4

ok, i'm trying that now

Answer 5

1 + 2 a + a^2 - b^2 = 0
2 ab - 2 b = 0

Answer 6

{{a -> -1, b -> 0}, {a -> -1, b -> 0}, {a -> 1, b -> -2}, {a -> 1,
b -> 2}}

Answer 7

-1, 1-2i,1+2i

Answer 8

Ok, thx! :)