complex number question (1 Viewer)

[cormglakes]

let z=cosx + isinx

solve z^4 - 4z^3 + 2z^2 - 4z+1 = 0

 

[Qeru]

let z=cosx + isinx

solve z^4 - 4z^3 + 2z^2 - 4z+1 = 0

But

So the problem becomes:

which is a 3U problem (remember to take only the first 4 unique solutions).

OR

notice

So the problem becomes:

Which is simply a quadratic in

 

[cormglakes]

But

So the problem becomes:

which is a 3U problem (remember to take only the first 4 unique solutions).

and then after I get cosx=0 --> z= i & -i
and cosx=2 --> how do I find the other 2 roots?

 

[CM_Tutor]

At this point, notice we have a quadratic in ? So...



and the equation has two real roots, , and two purely imaginary roots

 

[CM_Tutor]

and then after I get cosx=0 --> z= i & -i
and cosx=2 --> how do I find the other 2 roots?

In taking there is an assumption made that all solutions in will have modulus of 1 and satisfy . This is not true for the two real solutions so you run into a problem.