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complex number question (1 Viewer)

Qeru

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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

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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

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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.
 

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