+0  
 
0
76
2
avatar+82 

done

 Mar 19, 2020
edited by rubikx2910  Apr 15, 2020
 #1
avatar+111360 
+3

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 )

 

 

cool cool cool

 Mar 19, 2020
 #2
avatar+82 
+1

done

rubikx2910  Mar 20, 2020
edited by rubikx2910  Apr 15, 2020

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