Question

Sa se calculeze t1 si t2: z⁶-z³+1+i=0

Answer 1

[tex]z^6-z^3+1+i=0\\ z^3=t\\t^2-t+1+i=0\\ \Delta=b^2-4ac=(-1)^2-4*1*(1+i)=1-4(1+i)=1-4-4i=\\=-3-4i=-(3+4i)\\\sqrt{-(3+4i)}=\sqrt{(3+4i)i^2}=i\sqrt{3+4i}\\ t_1= \frac{-b-\sqrt{\Delta}}{2a} =\frac{1-i\sqrt{3+4i}}{2}\\ t_2= \frac{-b+\sqrt{\Delta}}{2a} =\frac{1+i\sqrt{3+4i}}{2}\\ [/tex]