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But when i got down to it, it ended up being:

2*cuberoot(3298 +/- i*627550*sqrt(5))

that gives r = 12534*sqrt(12534)

and a theta of 89.865 yada yada.

which means that the cube root is 97 +/- i*55.9016 or so. Mult by 2, and you get 194 +/- i*111.80 or so.

I got as far as that, and that's where my question came in...how did/do you drop the imaginary part so that you could represent all that above as a positive integer???

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But when i got down to it, it ended up being:

2*cuberoot(3298 +/- i*627550*sqrt(5))

that gives r = 12534*sqrt(12534)

and a theta of 89.865 yada yada.

which means that the cube root is 97 +/- i*55.9016 or so. Mult by 2, and you get 194 +/- i*111.80 or so.

I got as far as that, and that's where my question came in...how did/do you drop the imaginary part so that you could represent all that above as a positive integer???

I think the bolded part is the problem here

I assume you meant that

cuberoot(3298 + 627550 * sqrt(-5)) + cuberoot(3298 - 627550 * sqrt(-5)) = 2 * cuberoot(3298 +/- i*627550*sqrt(5))

The above isn't true because you can not distribute outside the cuberoot sign. The straight forward approach would be to compute all 3 roots of cuberoot(3298 + 627550 * sqrt(-5)), then compute all 3 roots of cuberoot(3298 - 627550 * sqrt(-5)). Looking at those, you'll probably find a pair such that their sum is a positive integer with no imaginary part. Computing the 3 cube roots is easier if you draw it on a graph.

Edited by bushindo
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But when i got down to it, it ended up being:

2*cuberoot(3298 +/- i*627550*sqrt(5))

that gives r = 12534*sqrt(12534)

and a theta of 89.865 yada yada.

which means that the cube root is 97 +/- i*55.9016 or so. Mult by 2, and you get 194 +/- i*111.80 or so.

I got as far as that, and that's where my question came in...how did/do you drop the imaginary part so that you could represent all that above as a positive integer???

I'm not sure what 2*cuberoot(3298 +/- i*627550*sqrt(5)) means. But the original problem has it as

cuberoot(3298 + i*627550*sqrt(5)) + cuberoot(3298 - i*627550*sqrt(5)). When I did the problem I started by cubing the monster then staring at the result and saw a way to simplify (without De Moiuvre's formula, by the way). I ended up with a cubic equation which I could solve.

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I think the bolded part is the problem here

I assume you meant that

cuberoot(3298 + 627550 * sqrt(-5)) + cuberoot(3298 - 627550 * sqrt(-5)) = 2 * cuberoot(3298 +/- i*627550*sqrt(5))

The above isn't true because you can not distribute outside the cuberoot sign. The straight forward approach would be to compute all 3 roots of cuberoot(3298 + 627550 * sqrt(-5)), then compute all 3 roots of cuberoot(3298 - 627550 * sqrt(-5)). Looking at those, you'll probably find a pair such that their sum is a positive integer with no imaginary part. Computing the 3 cube roots is easier if you draw it on a graph.

The equation has 4 answers, 2 of which are the same...

cuberoot(3298 + 627550 * i * sqrt(5)) + cuberoot(3298 + 627550 * i * sqrt(5))

cuberoot(3298 + 627550 * i * sqrt(5)) + cuberoot(3298 - 627550 * i * sqrt(5))

cuberoot(3298 - 627550 * i * sqrt(5)) + cuberoot(3298 + 627550 * i * sqrt(5))

cuberoot(3298 - 627550 * i * sqrt(5)) + cuberoot(3298 - 627550 * i * sqrt(5))

The key answers are the middle two...that's where you wind up with principal roots of 97 + 55.901i + 97 - 55.901i

= 194

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