+128408 Expanding (√3 - i)^10 we have
(√3)^10 - C(10, 1)(√3)^9(i) + C(10, 2) (√3)^8 (i)^2 - C(10,3)(√3)^7(i)^3 + C(10,4)(√3)^6(i)^4
- C(10, 5)(√3)^5(i)^5 + C(10, 6)(√3)^4(i)^6 - C(10, 7)(√3)^3(i)^7 + C(10,8)(√3)^2(i)^8 - C(10, 9)(√3)(i)^9
+ i^(10
Simplify
3^5 - 10 (3)^4 (√3)i + 45(3)^4(i)^2 - 120(3)^3(√3)(i)^3 + 210 (3)^3(i)^4 - 252(3)^2(√3)(i)^5
+ 210(3)^2(i)^6 - 120(3)(√3)i^7 + 45 (3)i^8 - 10 (√3)i^9 + i^10
243 -810(√3)i + 3645 (-1) - 3240(√3)(-i) + 5670 (1) - 2268(√3)i + 1890 (-1) - 360(√3) (-i)
+135(1) - 10√3i - 1
[243 - 3645 + 5670 - 1890 + 135 -1 ] + [ -810√3 - 2268√3 - 10√3] i + [ 3240√3 + 360√3] i
512 + [ -810 - 2268 - 10 +3240 + 360] √3 i
512 + 512√3 i
So
(a, b) = (512, 512√3 )
