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decide the valuei'm not sure about value of z^4+1/z^4 i only know that z^3=1
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If z^3 = 1, then z^3 - 1 = 0
We'll re-write the difference of cubes as:
z^3 - 1 = (z - 1)(z^2 + z + 1)
If z^3 - 1 = 0, then (z - 1)(z^2 + z + 1) = 0
We'll re-write the sum to be calculated as:
z^4 + 1/z^4 = z*z^3 + 1/z*z^3
But z^3 = 1 (1)
z^4 + 1/z^4 = z + 1/z
We'll multiply by z:
z^4 + 1/z^4 = (z^2 + 1)/z
But z^2 + z + 1 = 0 => z^2 + 1 = -z
z^4 + 1/z^4 = -z/z
z^4 + 1/z^4 = = -1
The requested value of the sum z^4 + 1/z^4 = -1.
Posted by giorgiana1976 on April 9, 2011 at 8:33 AM (Answer #2)
High School Teacher
If z^3 = 1 then let y = z^4 + 1/ z^4
Where y is the value you need to be sure of.
For z^3 = 1, z = 1^0.33 recurring.
1 raised to any power is equal to 1 therefore:
z = 1
Evaluating y = z^4 + 1/z^4
= 1^4 + 1/1^4
= 1 + 1/1
= 1+1 = 2
Posted by nessus on July 12, 2011 at 9:48 PM (Answer #3)
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