a) z= 1+i= a+bi
scriem z sub forma trigonometrica
z= r (cos t+ i sin t) unde r=√a²+b² si t= arctg b/a
deci z= √2 (cos π/4+i sin π/4)
=> z⁴= (√2)⁴ (cos 4π/4 +i sin 4π/4)= 4 (-1)=-4
z⁴+z conjugat= (-4+1+i) conjugat= -3-i ∉R
b) 1/z= z la -1= 1/√2 (cos -π/4+ i sin-π/4)= 1/√2 (1/√2- 1/√2 i)= 1/2 -1/2 i
x=1+√2
x- 1/z= 1+√2- 1/2 +1/2 i
