Question

calculati (rad 3 -i)^8 (-1+i rad 3)^12

Answer 1

Răspuns:

Explicație pas cu pas:

i^2 = -1,  i^4 = (-1)^2 = 1

E = ((√3 -i)(-1 +i√3))^8*(-1 +√3)^4

(√3 -i)(-1 +i√3) = -√3 +3i +i +√3 = 4i

(-1 +i√3)^2 = 1 -i2√3 -3 = -2(1 +i√3)

(-1 +i√3)^4 = (-2(1 +i√3))^2 =

 4(1 +i2√3 -3) = -8( -1 +i√3)

E = (4^8*i^4*i^4)( -8( -1 +i√3)) =

4^8*1*1(-8( -1 +i√3)) =

-2^16*2^3( -1 +i√3)=

-2^19( -1 +i√3)