Question

Find the first three iterates of the function f(z) = 2z + (3 - 2i) with an initial value of z0 = 5i.

Answer 1

Answer:

The three iterates are:

• $z_1=8i+3$

• $z_2=14i+9$

• $z_3=26i+21$

Step-by-step explanation:

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

$f(z) =2z+(3-2i)$ with an initial value:

$z_0=5i$

The first iterate is:

$z_1=f(z_0)=2z_0+(3-2i)\\\\z_1=2\times 5i+3-2i\\\\z_1=10i-2i+3\\\\z_1=8i+3$

Now, the second iterate is:

$z_2=f(z_1)=2z_1+(3-2i)\\\\z_2=2\times (8i+3)+3-2i\\\\z_2=16i+6+3-2i\\\\z_2=14i+9$

Third iterate is:

$z_3=f(z_2)=2z_2+(3-2i)\\\\z_3=2\times (14i+9)+3-2i\\\\z_3=28i+18+3-2i\\\\z_3=26i+21$

Answer 2

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