Trig/Pre-Cal question on complex number/planes?
f(z)=z^2+c
c=3-2i
Find a complex number v that is in the escape set. Find a complex number w that is in the prisoner set. Graph the first five iterations of both v and w and connect them with line segments.
Completely lost. Don't understand. Tired of staring at it while being clueless -_-Help? Process? How to graph? Anything? /: Thank you! You're saving me from a a longer-lasting headache!
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I agree with the other responder that website gives some good information. However, I can offer a bit more to the process.
If you pick a value for Z of the form (a +bi) the f(Z) = (a² - b² + 3) - (2ab + 3)i then if e^ (a² - b² + 3) < 2 it will probably be a member of the prisoners; if it is greater than 2, then it is a member of the escape set.
You need to check at least 5 iterations where you pick a Z0, Z1 = f(Z0), Z2 = f(Z1)...
Checking each for e raised to the real part greater than 2 or less than 2.
you try to sparkling up for the linked fee of b, brilliant? if so: a million. b^3=a million/5, so b=(a million/5)^(a million/3) 2. b^8=a million/3, so b=(a million/3)^(a million/8) 3. b^5=3/7, so b=(3/7)^(a million/5) The parentheses are significant. Your answer in basic terms isn't brilliant in case you do not use the parentheses at the same time as inputting the expressions on your calculator. you may also use logarithms when you're conscious of them. as an party: b^3=a million/5 3log(b)=log(a million/5) log(b)=(a million/3)log(a million/5) b=10^{(a million/3)log(a million/5)}
http://www.jcu.edu/math/vignettes/Julia.htm
explains what this stuff is better than I can.
As I've not had much contact with this or complex stuff, I'm not sure how to find v and w aside from trial and error.