# complex number question (1 Viewer)

#### cormglakes

##### New Member
let z=cosx + isinx

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

#### Qeru

##### Well-Known Member
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

##### New Member

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

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

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

#### CM_Tutor

##### Moderator
Moderator
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.