Respuesta :

3 because the 2z minus the 3 gives you 1 rounded

Answer:

The three iterates are:

  • [tex]z_1=8i+3[/tex]
  • [tex]z_2=14i+9[/tex]
  • [tex]z_3=26i+21[/tex]

Step-by-step explanation:

We are asked to find the first three iterates of the function:

[tex]f(z) =2z+(3-2i)[/tex] with an initial value:

[tex]z_0=5i[/tex]

The first iterate is:

[tex]z_1=f(z_0)=2z_0+(3-2i)\\\\z_1=2\times 5i+3-2i\\\\z_1=10i-2i+3\\\\z_1=8i+3[/tex]

Now, the second iterate is:

[tex]z_2=f(z_1)=2z_1+(3-2i)\\\\z_2=2\times (8i+3)+3-2i\\\\z_2=16i+6+3-2i\\\\z_2=14i+9[/tex]

Third iterate is:

[tex]z_3=f(z_2)=2z_2+(3-2i)\\\\z_3=2\times (14i+9)+3-2i\\\\z_3=28i+18+3-2i\\\\z_3=26i+21[/tex]

Otras preguntas