Question

Sa se rezolve in C ecuatia : z la a 5 a egal cu -i ... Va rog repede !

Answer 1

z⁵   = - i = 0  -  i 
punctul  A (  0 , - 1)  ⇒    α =270° = 3π /2 
| 0 - i | = √( -1)² = 1 
z⁵  = cos3π/2 + isin3π/2 
rad .   z = cos ( 3π/2  +2kπ ) / 5 + isin ( 3π/2 + 2kπ ) / 5 
k= 0,1,2,3,4 
k=0       z₀  = cos3π /10 + isin 3π/10 
k=1       z₁  = cos ( 3π /2  + 2π ) /5 + isin( 3π/2 + 2π) /5 =
                    =  cos7π /10 + i sin 7π/10 
k =2        z₂ = cos ( 3π /2 + 4π) / 5  + isin( 3π/2 + 4π ) /5 
                       = cos11π /10  + isin11π/10 
k=3         z₃  =  cos 3π/2  + i sin3π /2
k = 4       z₄  = cos 19π / 10  + isin19π/10