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henpenBest ResponseYou've already chosen the best response.0
\[\left z1 \right+\left z+1 \right=4\] Which turns into the messy \[\sqrt{(a1)^2+b^2}+\sqrt{(a+1)^2+b^2}=4\] Which I have no idea about how to solve graphically.
 one year ago

henpenBest ResponseYou've already chosen the best response.0
(And by 'graphically' I mean plotting the possible values of z on the complex plane)
 one year ago

henpenBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=sqrt%28%28x%2B1%29%5E2%2By%5E2%29%2Bsqrt%28%28x1%29%5E2%2By%5E2%29%3D4 Can anyone explain why the graph is an ellipse?
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
 a + bi  1 + a + bi + 1 = 4
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
 (a 1) + (b)i  +  (a+1) + (b)i  = 4
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Now let me find the modulus which is given by sqrt( re(z)^2 + Im(z)^2)
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[\sqrt{(a +1)^2 + b^2} + \sqrt{(a1)^2 + b^2} = 4\]
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Then you should square both sides
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Actually that will be hard
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
So move one of the square roots on the left then square both sides
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[(\sqrt{(a+1)^2 + b^2} )^2= (4  \sqrt{(a1)^2 + b^2})^2\]
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Which will give you this
 one year ago

henpenBest ResponseYou've already chosen the best response.0
There's still a horrible square root sign there, though.
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[(a+1)^2 + b^2= 16  8\sqrt{(a1)^2 + b^2} + (a1)^2 + b^2\]
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
I will get rid of it soon
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Ok now i am going to cancel some stuff and simplify this equation
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[a^2 + 2a + 1 + b^2 = 16  8\sqrt{(a1)^2 + b^2} + a^2  2a + 1 + b^2\]
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Now i can simplify further
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[4a 16 = 8\sqrt{(a1)^2+b^2}\]
 one year ago

henpenBest ResponseYou've already chosen the best response.0
4a16=8sqrt(a^22a+1+b^2)
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Now I am going to square both sides again
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[(4a 16)^2 = 64((a1)^2 + b^2)\]
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Finally we have no more square roots
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Now i am going to expand
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
\[16a^2 128a + 256 = 64 a^2 128a + 64 + 64b^2)\]
 one year ago

henpenBest ResponseYou've already chosen the best response.0
it ends up as 192=48a^2+64b^2 I think
 one year ago

henpenBest ResponseYou've already chosen the best response.0
That actually agrees with the wolfram link I posted earlier. Thanks very much I had little idea how to deal with square roots efficiently before!
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Final step: complete the square on a term
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
Sorry yeah that was the answer 192 = 48a^2 +64b^2
 one year ago

baddinlolBest ResponseYou've already chosen the best response.1
And thats an eclipse.
 one year ago
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