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how about just
Re^itheta = 7+24i

I don't know

hm thats not nice

|dw:1434880616850:dw|

the angle seems to be exact in degrees

oh thats a nice trick

I'm getting that it's equal to both \[1-3i\] and \[-1+3i\]

there could be 2 answers

going forward and backwards

|dw:1434881253505:dw|

both of them look about right

and then sqrting the radius

then convert that to cartesian

or would that get messy with e and pi in that mix

Is there a visual way in which we can consider the square root of -8-6i as being 1-3i or -1+3i.

I guess that's what you did, you drew it then rotated in either direction

yeah

and then took the square root of the length

right ya squaring i mean not doubling, i confuse those 2

Yeah I gotcha, ok here's a good one looks kinda simple though http://prntscr.com/7ji5ww

we could see they are all orthogonal or

or just take dot products and that bs

is there a way to rewrite all these points in a rotated dimension, like a simple way

they just gave us points ah

Points, vectors, whatever

yea this still works i guess

that will turn them into vectors so we can do this agian

|dw:1434882161951:dw|

|dw:1434882255217:dw| Since those are the midpoints on a square, this is a square.

Their solution is ugly as crap: http://www.exampleproblems.com/wiki/index.php/CV19

|dw:1434882335886:dw|

oh thats gross they are writing it out as lines lol

haha

Yeah they're doing it the way I would program a computer to do it maybe, but I have a brain tyvm

this way u can break out of the loop as soon as one if it fails

yeah, that wud be nice, but we wont always get lucky

What do you mean why not?

they can give us annoying points that arent centered

They don't have to be centered for this to work

find we have to take the double diagonal and reposition that intersection as the origin

Woah! I just saw something miraculous

If it's a square then we can add up all the 4 complex numbers to get the center of the square.

wait really

Then we subtract this from the 4 numbers to center it.

no matter where the squre is placed?

It's like vectors in equilibrium.

But the equilibrium is the center displaced

|dw:1434883019314:dw|

Then we can literally square any of the numbers we have to get the other 3, after we normalize them.

|dw:1434883081383:dw|

yaa
thats what i mean though, u wont get nice vertices though

watch, I'll do it.

ohh wait! ur saying additiong of these 4 vectors will give u center, i can see it kind of :O

woah thats cool, it makes sense it has to go toward the center

Yeah this is the best way for a computer to do it too for any polygon.

the farther away from center u are the more u are pulled to the otehr vertices

this gives us a much simpler way of solving the square question now

this works for all regular polygons

Yeah

Wait this doesn't quite work hahaha

It should be the average of the points not just the sum of the points.

ya i was just looking at that lol

|dw:1434883586373:dw|

What could be sexier?

|dw:1434883777297:dw|

like thats an easy one to see that fails for sure

No, that doesn't fail

why not

\[\frac{0+2-2i+(2-2i)}{4}=1+i\]

oh ya i mean not this, the one wiht just adding

|dw:1434883967181:dw|

this is the same thing just said a bit differently

with the 4 vectors 2 at a time share a b c d

True but your method fails if the square looks like this: |dw:1434884123357:dw|

oh truee

well its something thoughj still as long as the point is somethere in the square

|dw:1434884274366:dw|

lol

No offense....

lolol

Yeah but dan do you not understand what I said before?

which one?

oh ya i can see that one works no matter what

im just seeing if there is a less computation way in some cases

not that it matters lol

I think this is the least computational way unless you wanna do it their gross way lol

well like (-a+b, -c+d) is center is slightly faster than (a,c) + (a,d) + (b,d)+ (b,c)/ 4

I don't understand how your calculation is realistic though

why not

In that example what is a,b,c, and d if there are coefficients 2,1,4,3,5,0 ?

ohh i see the problem okayy

ah okay that makes sense

the rotations

they should allow rotation in the draw tool, that give so many more options

what do you mean reguarly spaced and subtract the center vector

|dw:1434885527859:dw|

that vector?

ah okay that makes sense

once u subtract the center vector every point is share by 2 vectors

every componnent of the point

wait no

are u sure this formula works

does it have to more a multiple of 4 more than times 1

have to be*

|dw:1434886153355:dw|

or actually 4 at a time

No, rethink this, you're on the right track though.

|dw:1434886388250:dw|