Question

Okay, I couldn't get any help last night so I was wondering if anyone would help me today.

Find the first three output values of the fractal-generating function f(z) = z^2 − 1 + 2i. Use z = 0 as the first input value.

Answer 1

@*Insert Name Here* Can you please help?

Answer 2

first three output values... would that be z=0, 1, and 2?

Answer 3

I don't know.

Answer 4

no, it's a feedback loop.

\[z_0 = 0\Rightarrow f(z_0) = (0)^2-1+2i=-1+2i \Rightarrow z_1 = -1+2i\]

now find f(z_1) to get z_2, etc.

fractals are feedback loops. you feedback in what you get out. get it?

Answer 5

\[z_n = f(z_{n-1})\]

Answer 6

hello... you there?

Answer 7

you good @Burningitdown ?

Answer 8

Sorry, Trying to figure it out.

Answer 9

@pgpilot326

Answer 10

did you get the next output?

Answer 11

I don't know how, really.

Answer 12

okay, i'll walk you through it. \[z_2=f(z_1) = z_1^{2}-1+2i\text{, remember }z_1=-1+2i\]

do you know how to multiply complex numbers?

Answer 13

No.

Answer 14

@pgpilot326 Again, really sorry for how long it takes me. So much lag.

Answer 15

no worries.

\[(a+bi)(c+di)=(ac-bd)+(ad+bc)i\]

Answer 16

Uh..okay.

Answer 17

\[\text{Ex. } (1+2i)(3+4i)=(1\cdot3-2\cdot4)+(1\cdot4+2\cdot3)i = -5+10i\]

Answer 18

Okay.

Answer 19

so in your case you'll have this...
\[z_0 = 0\Rightarrow z_1=f(z_0) = 0^2-1+2i=-1+2i\]
\[z_1 = -1+2i\Rightarrow z_2=f(z_1) = (-1+2i)^2-1+2i=(-3-4i)-1+2i=-4-2i\]

Answer 20

\[=-4-2i\]

Answer 21

Okay.