Question

E4. Toate subpunctele dacă se poate. Sau măcar o idee de rezolvare. :)
Ofer coroniță.

Answer 1

z^4-16=0
(z²-4) (z²+4)=0
(z-2) (z+2)(z-2i) (z+2i)=0
z1,2=+-2
z3,4=+-2i
 as simple as that!!

z³=i=cosπ/2+isinπ/2
z1=cosπ/6+isinπ/6
z2=cos(π/6+2π/3)+isin(5π/6)=cos5π/6+isin5π/6
z3=cos(π/6+4π/3) +isin(9π/6)=cos(3π/2)+isin3π/2=-i

z^6=-1+i=√2(cos3π/4+isin3π/4)
 cu Moivre ca mai sus, modulul fiind radical ord 6 din (√2)= 2*(1/12)
iar argumenteler fiind (3π/4+2kπ)/6 cu k=0;1;2...5

z^9=1=cosπ+isinπ
z1=cosπ/9+isinπ/9
z2= cos (π/9+2π/9)+isin (π/9+2π/9)=cosπ/3+isinπ/3
.............................................................................................
z9=cos(π/9+16π/8)+isin(π/9+16π/9)= cos17π/9+isin17π/9