Answer this only if you are brave enougth?

Question

I asked a maths question here a week or two ago and it was answered correctly within about 15 minutes, so I have decided to ask a much harder question.
In school I used to solve similtanious equations, since school I have learned about complex numbers, I have decided to mix the two areas to produce a similtanious complex equation, the first to give a correct answer gets the 10 points :

x squared + y + 40 + 32 i = -5
x + y squared + 53 + 107 i = 10 i

solve both x and y (both are complex numbers)
hopefully this question is hard enougth to keep you going for longer.
Only try this if you want a challenge.

No girth_03 both x and y can be solved and by solved I mean are both equal to complex numbers (without any other variables in, ie no x or y on the right side of the = sign)

By the way drawing these equations would probably be even more complicated, as each of them would be a 2 dimensional plain lying in a four dimensional space, as there are 4 variables in each equation (ral part of x, real part of y, imaginary part of x and inaginary part of y). Where the two plains intersected would be the answer(s) to the similtanous equations.

Eulercrosser if a quartic is an equation with a 4th power in it then you are heading in the right direction, because when I solved it I did have to solve such an equation.

bequalming I delibratly made it difficult because the last complex problem I gave was solved way too fast, whoever gets this one right would have earned their 10 points.

I have seen many solutions that are half completed but there is an answer for x and y which are just complex numbers of the form a+bi

to greencaddyman. I know I have the answer, but some people like to solve puzzles and problems just to exercise their brain, it doesn`t matter that the problem has allready been solved by others, if you don`t like doing this, then you just ain`t a puzzle-problem solving person.

To Marshmallow, you got your 2 points, really I expect this problem to be solved by someone over 10, I never knew about complex numbers untill I was over 15.

Vivek you say its not hard but haven`t given me the complex numbers that satisfy x and y in the equations.

And by the way it didn`t really matter that i spelt simiultaneously wrong, because everyone who read it knew what i meant. The spell checker only checks the questions, not the added details.

Answer 1

I recommend making it easier. x²+y=m; x+y²=n. m is -45-32i; n is -53-97i. Then I got y²=m²-2mx²+x^4.
x+m²-2mx²+x^4=n. Or x^4-2mx²+x+ (m²-n) = 0.

Answer 2

Answer THIS only if you are brave enough. Do you need the answer to this or do you already have it. You said you already figured out what the answer is, so you must have solved the quartic. So the next question restricted only for the brave is, why did you ask a question that you already knew the answer to? Is getting this answer part of your job or something that earns you money? You said that you have asked people to solve other problems like this, so that means that you spent at least 10 points asking questions that you already knew the answer to. I ask again, what is the point in that. From questions like this, people can already tell that you don't have much of a life outside of asking and answering these type of questions. Get a hot girl that does'nt resemble a librarian, a purpose other than solving things that have already been solved, and a social life that revolves around more than a keyboard, or getting these answers will be the most exciting thing in your life, and that is pretty sad.

Answer 3

I hate solving the quartic :)

back to the football match; work on this later :)

hehe, I like that one guys answer. I bet he doesn't realize that the most popular question in the math area is 1+1=1?

I shall retire from this problem. {Beer}∩{solving a quartic in complex variables}=Headache

Germany destroyed Ecuador!!!

Answer 4

There are formulas for solving the following equations: ax+b=0; ax^2+bx+c=0, ax^3+bx^2+cx+d=0 and ax^4+cx^3+dx^2+ex+f=0. Memorizing these formulas is not a challenge, is not puzzling or fun and, for the last two, is not even useful.

Answer 5

it's not hard or complicated..but lengthy..
x^2+y= 35-32i
x+y^2 = -53-97i
hence x^2= 35-32i-y=(-53-971-y^2) ^2
take y= a+ib
put in this..
we have then
35-32i- a-ib = (-53-97i- (a+ib)^2 ) ^2
= (-53 - 97i- a^2 +b^2 + 2aib)^2
then follow this step..
expand this..
equate the real and imaginary parts
we will have 2 equations for that..solve them..
get a and b..
obtain x from this..
there will be two values for both x and y..

Answer 6

Quartics are a torture, not a challenge. Just like e.g. inverting a large matrix is. Number-crunching exercises like that do not make you smarter.

Answer 7

I have no idea.I am only 10 years.I dont even know what that means.Im just in for the points.

Answer 8

y = -x squared - 45 -32i
x = -y squared - 53 - 97i

is that all you're looking for?

Answer 9

You should have spent more time working on your spelling "SIMULTANEOUSLY', while studying these complex math problems.

Answer 10

Sorry, waist of time.