Question

$( \frac{1 + i \sqrt{7} }{2}) {}^{4} + ( \frac{1 - i \sqrt{7} }{2}) {}^{4}$
cu cat este egal?

Answer 1

( 1 +i√7 /2 )⁴ =( 1 +i√7 /2 )²·( 1 +i√7 /2 )² => (1 +i√7 )²=1 +2i√7 +i²√7=1-7 +2i√7=-6 +2i√7 <=> (1 +i√7 /2)² =-6 +2i√7 /4 ;prin analogie obtinem ( 1 -i√7 /2 )²=-6 -2i√7 /4 => ( 1 +i√7 /2 )⁴ +( 1 +i√7 /2 )⁴=( 8 -24i√7 /16 ) +( 8 +24i√7 /16)=8/16 +8/16=16/16=1 <=> ( 1 +i√7 /2)⁴ +( 1 -i√7 /2)⁴ =1 .