find all z in C that verify simultaneously:
|z|² + |z| - 2 = 0
z^8 + z^6 + z^4 + z^2 = 0
Of the first equation I know that 1 is a root.
And I think i is a solution for the second one.
But I cant find a convincing solution.
Find all that satisfy simultaneously: .
The first equation factors: .
And we get: .
. . (A magnitude cannot be negative.)
The second equation factors: .
And we have: . . . . which does not satisfy the first equation
But these do:
And so do these: