SOLUTION: Find all the solutions of the equation z˄6 + (2 + 2i)z˄3 + 2i = 0.

SOLUTION: Find all the solutions of the equation z˄6 + (2 + 2i)z˄3 + 2i = 0.

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Question 1123448: Find all the solutions of the equation z˄6 + (2 + 2i)z˄3 + 2i = 0.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Let

, then

Using the Quadratic formula:

with a multiplicity of 2. Verification of this step left as an exercise for the student.

Hence

But this must be multiplied by the three cube roots of unity to obtain the three roots of the cubic which, considering the multiplicity of the quadratic in

gives the 6 roots of the original 6th-degree equation.

John

My calculator said it, I believe it, that settles it

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