Show that -i is in the Mandelbrot Set

[vorcil]

1a:
show w = -i is in the mandelbrot set
show that -1-i is not in the mandelbrot set
is w= -0.1226 + 07449i in the mandelbrot set, first show that z2 =0

don't know how to do any of them

i tried, -(squareroot-1) ^2 = --1, + squareroot -1
idk

 

[Mark44]

What exactly does it mean for a complex number to be in the Mandelbrot set? You need to have this definition in order to tell whether a give complex number is or isn't in this set.

I don't understand some of the things you have written:
"z2 = 0" Do you mean z² = 0? If you don't know how to use the LaTeX controls, you can write this like so: z^2 = 0.

"-(squareroot-1) ^2 = --1, + squareroot -1"
I don't understand this at all, but you can write sqrt(-1) to mean the square root of -1 (which is i).

 

[vorcil]

For a number to be in the mandelbrot set, it means that it stays within the boundary of that circle thing, and it repeats in a sequence, where a number not in the mandelbrot set doesn't stay in the boundary and doesn't repeat it's sequence

from that formula, Z₁ = Z₀^2 + Z₀ (each time 0 is incremented by 1

 

[HallsofIvy]

This is very poorly written. If you want to be a good itexematician you must learn to be precise and clear!

For a number to be in the mandelbrot set, it means that it stays within the boundary of that circle thing, and it repeats in a sequence, where a number not in the mandelbrot set doesn't stay in the boundary and doesn't repeat it's sequence

You used the word "it" four times without saying what "it" refers to! (And with two different meanings!) You don't say what "that circle thing" is. You don't say what sequence you are talking about and you don't say what "stay in the boundary" means. What you should be saying is that a certain sequence remains bounded. And I can find no requirement that it "doesn't repeat its sequence". If a sequence eventually repeats, it certainly remains bounded.

from that formula

from what formula?

, Z₁ = Z₀^2 + Z₀ (each time 0 is incremented by 1

Okay, this is the"formula" you referred to above and that gives the sequence you are referring to. But as given that implies that Z₂= Z₁²+ Z₁ which is incorrect. You want Z_n+1= Z_n²+ c for a fixed number c and Z₀= c. When you ask "is -i in the Mandelbrot set" you are taking c= -i. Then $Z_0= -i$, $Z_1= (-i)^2+ (-i)= -1- i$, $Z_2= (-1+1)^2+ (-i)= i$, $Z_3= (i)^2+ (-i)= -1-i$ again!

It looks to me like that becomes repeating.

 

[vorcil]

Sorry, thanks =]
I know how to use the mandelbrot set now(I think),

The mandelbrot set was not in my math book, and i didn't take notes during my lecture because i thought it was in the my mathematics book