Question

Sa se rezolve in c ecuatia
Z^4=-16

Answer 1

Răspuns:

Explicație pas cu pas:

Moivre sa traiasca ( in eter(n))!!

z^4=-16=16(cosπ+isinπ)

16^(1/4)=2

z1,2,3,4=2(cos(π+2kπ)/4+isin(π+2kπ)/4))...k∈{0;1;2;3}

z1=2(cos(π/4)+isin(π/4))=2(√2/2+i√2/2) =√2+i√2

z2=2(cos (3π/4)+isin (3π/4))=...=-√2+i√2

z3=2(cos(5π/4)+isin(5π/4))=...=-√2-i√2

z4=2(cos (7π/4)+isin(7π/4)=...=√2-i√2