Asked by Anonymous
What is the solution and magnitude of the following problem:
(x^4)-1=0
(x^3)+1=0
(x^3)-1=0
(x^6)-1=0
(x^6)+1=0
(x^4)-1=0
(x^3)+1=0
(x^3)-1=0
(x^6)-1=0
(x^6)+1=0
Answers
Answered by
Steve
x^4 = 1 = 1 cis 2π
x = 1 cis 2π/4 = 1cis π/2
Now add multiples of 2π/4 to that till you get all 4 roots.
You can verify, knowing that 1^4 = (-1)^4 = i^4 = (-i)^4 = 1
Do the others in like wise.
x = 1 cis 2π/4 = 1cis π/2
Now add multiples of 2π/4 to that till you get all 4 roots.
You can verify, knowing that 1^4 = (-1)^4 = i^4 = (-i)^4 = 1
Do the others in like wise.
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