SOLUTION: Which of these is the cube root of 1? 1/2- i sqrt3/2 1/2+ i sqrt3/2 -1/2 + i sqrt3/2 1- i sqrt3 1+ i sqrt3

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Which of these is the cube root of 1? 1/2- i sqrt3/2 1/2+ i sqrt3/2 -1/2 + i sqrt3/2 1- i sqrt3 1+ i sqrt3       Log On


   

Question 301200: Which of these is the cube root of 1?
1/2- i sqrt3/2
1/2+ i sqrt3/2
-1/2 + i sqrt3/2
1- i sqrt3
1+ i sqrt3





Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E3+-+1+=+0
%28x-1%29%2A%28x%5E2+%2B+x+%2B+1%29+=+0
x = 1
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A1=-3.

The discriminant -3 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -3 is + or - sqrt%28+3%29+=+1.73205080756888.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B1+%29


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It's -1/2 + i sqrt3/2
Also -1/2 - i sqrt3/2