perplexus.info :: Just Math : Find the Floor Difference

Find the Floor Difference (Posted on 2025-02-24)

Given that n is a small positive integer such that:
(√3+i)ⁿ=a, where a is a real number.

Find ⌊n-a⌋

Note: ⌊x⌋ is the floor of x, which is the greatest integer contained in x.

No Solution Yet Submitted by K Sengupta

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solution

| Comment 1 of 2

The complex number √3 + i has magnitude 2 and angle 30 degrees.

If n is a multiple of 6, then a will be a real number.

Let z = (√3+i)

Let n = 6

z^n = a = -2^6 = -64

n-a = 70

⌊n-a⌋ = 70

if n = 12 then a = +2^12 = 4096

n-a = ⌊n-a⌋ = -4084

If I am interpreting the problem correctly.

Posted by Larry on 2025-02-24 11:19:33

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