Question

Vreau si eu punctele i), j) si k) va rog!

Answer 1

i)

r²=1/2+1/4=3/4

r=|z|=√3/2

arg redus = arctg((1/2):(√2/2))=arctg(√2/2)

z=√3/2 (cos(arctg(√2/2)+isin(arctg(√2/2)))

j) |z|²=3/4+1/4=1⇒r=|z|=1

tg arg redus= (1/2) :(-√3/2)) =(-1/√3)=-π/6 cum cos 9arg redus) <0 si sin (arg redus) >0 ⇒arg redus∈(π/2 ;π) deci arg redus=π/2+π/6=4π/6=2π/3

z=cos(2π/3) +isin(2π/3)

k) analog observa  ca |z| =√1=1 si arg redus =2π-π/6=11π/6 (cosinusul e pozitiv si sinusul e negativ, deci cadranul IV

z=cos(11π/6)+isin(11π/6)