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.
On the Argand plane, sqrt(3)+1 is at the 30° angle and has an absolute value of 2. The value of a becomes real (and is an integer) when n is a multiple of 6 and is negative for odd multiples of 6 and positive for even multiples of 6.
The absolute values are the respective powers of 2. When n is 6, a is -2^6. This is already an integer, so the floor function does not affect it.
n a n - a
6 -64 70
12 4096 -4084
18 -262144 262162
24 16777216 -16777192
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Posted by Charlie
on 2025-02-24 12:10:24 |
solution
