Find the first three iterates of the function f (z) = 2z + (3 - 2i) with an initial value of z0 = 4.

First Iterate: 11-2i

Second Iterate: 25-6i

Third Iterate: 53-14i

Step-by-step explanation:

Given:

f (z) = 2z + (3-2i)

And

z_0=4

For the first iterate we have to put the value of z0 into the function in place of z.

First Iterate:

z_1=f (z_0) = 2z_0 + (3-2i)

=2 (4) + (3-2i)

=8+3-2i

=11-2i

Second Iterate:

For the second iterate we have to put the value of z1 into the function in place of z.

z_2=f (z_1) = 2z_1 + (3-2i)

=2 (11-2i) + (3-2i)

=22-4i+3-2i

=25-6i

Third Iterate:

For the third iterate we have to put the value of z2 into the function in place of z.

z_3=f (z_2) = 2z_2 + (3-2i)

=2 (25-6i) + (3-2i)

=50-12i+3-2i

=53-14i

Answer:d

Step-by-step explanation:

Cuz