Forgot your password?
ohhhh, ok now this all makes more sense. I was just going off of trying to solve it before which didn't lead to much . Do you know all of these formulas and how to use them just by memory? Also I do recall theta after looking at one, we just always used it to refer to an angle whose value is unknown before.
I'm baffled at how you converted z to r*e^(i*t) , also is r another variable? And where did e come from ;-;.
Also meant to write that one root out as (-1-i)(-1)^1/3, and (1+i)(-1)^2/3, I think those are equal to each other lul. I also never learned about theta yet :S
oh I wrote it wrong here, the original equation was
z^3 + 2 - 2i =0 not z^3 + 2 +2i :S (sorry I wrote that really late last night and copied it down again today when I retried it).
The method I used was to convert it to a cube so it would be easier to take the cube root.
Can't it also be done as
-2+2i = 1+3i-3-i = i^3+3i^2+3i+1
which can be simplified to three roots (1+i)^3, ((1+i)(-1)^1/3)^3, and ((1+i)(-1)^2/3)^3. They all should equal to -2+2i
then repluging it in gets z = ((1+i)^1/3)^3
which is z=1+i
Is there anything wrong with this ;-;
I am so tired, I just spent the past 5 hours helping my friend whose in college with Calculus. Currently 4am here . I didn't even understand half of it at first but I managed to learn as I was trying to explain it. I'm interested to see how you'd solve this problem though, Find all possible roots for z^3+2+2i=0. I'll reply in the morning as i've been up for around 24 hours now xD
Hmm... now I'm thinking about it.
How is the uniform norm calculated?
How do you compare sequences in L infinity? Having a bounded sequence there implies that L infinity is totally ordered, which means there has to be a way to do that...
You shall not pass!
Lift, pump, burn
Hail To The King
The Walking Innuendo