find all z in C that verify simultaneously:

|z|² + |z| - 2 = 0

and

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.

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- July 21st 2006, 03:13 PMkezmanfind all z
find all z in C that verify simultaneously:

|z|² + |z| - 2 = 0

and

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. - July 21st 2006, 05:49 PMSoroban
Hello, kezman!

Quote:

Find all that satisfy simultaneously: .

The first equation factors: .

And we get: .

. . (A magnitude cannot be negative.)

The second equation factors: .

Factor: .

Factor: .

And we have: . . . . which does__not__satisfy the first equation

But these do:

And so do these: