At the beginning of the 11th year, there would be 1,024,000
rabbits. 

At the beginning, there were 1000 rabbits. Also, there were
4000 rabbits at the beginning of third year which is equal
to 2828Z. Thus, Z = 4000/2828 i.e. 1.414 (the square root of 2) 

Note that 2828Z can be represented as 2000*Z*Z (Z=1.414),
which can be further simplified as 1000*Z*Z*Z*Z 

Also, it is given that at the end of 6 months, there were
1000Z rabbits. 

It is clear that the population growth is 1.414 times every
six months i.e. 2 times every year. After N years, the
population would be 1000*(Z^(2N)) i.e. 1000*(2^N) 

Thus, at the beginning of the 11th year (i.e. after 10
years), there would be 1000*(2^10) i.e. 1,024,000 rabbits.