Question

1+i√3
--------   --  (1-i)⁹⁺³=
1-i√3

Answer 1

Fractia o rationalizezi cu 1 + i$\sqrt{3}$ => ( 1 + 2i$\sqrt{3}$ - 3 ) / 4 = ( -2 + 2i$\sqrt{3}$ ) / 4 = ( - 1 + i$\sqrt{3}$ ) / 2;
( 1 - i ) ^943 =[ ( 1 - i )^2]^4721* ( 1 - i ) = ( - 2i )^471 * ( 1 - i ) = -2^471 * i^471 * ( 1 - i ) = - 2^471 * ( - i ) * ( 1 - i ) = 2^471( i + 1 ) ;
Daca intre fractie si paranteza este semnul de inmultire => 2^470 * ( 1 + i ) * ( - 1 + i$\sqrt{3}$ ) = 2^470 * ( - 1 - i +  i$\sqrt{3}$ - $\sqrt{3}$ )

Bafta!