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anonymous
 3 years ago
A complex question
anonymous
 3 years ago
A complex question

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anonymous
 3 years ago
Best 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0(And by 'graphically' I mean plotting the possible values of z on the complex plane)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0http://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?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0 a + bi  1 + a + bi + 1 = 4

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0 (a 1) + (b)i  +  (a+1) + (b)i  = 4

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Now let me find the modulus which is given by sqrt( re(z)^2 + Im(z)^2)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{(a +1)^2 + b^2} + \sqrt{(a1)^2 + b^2} = 4\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Then you should square both sides

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Actually that will be hard

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So move one of the square roots on the left then square both sides

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\sqrt{(a+1)^2 + b^2} )^2= (4  \sqrt{(a1)^2 + b^2})^2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Which will give you this

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0There's still a horrible square root sign there, though.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(a+1)^2 + b^2= 16  8\sqrt{(a1)^2 + b^2} + (a1)^2 + b^2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I will get rid of it soon

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Ok now i am going to cancel some stuff and simplify this equation

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[a^2 + 2a + 1 + b^2 = 16  8\sqrt{(a1)^2 + b^2} + a^2  2a + 1 + b^2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Now i can simplify further

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[4a 16 = 8\sqrt{(a1)^2+b^2}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.04a16=8sqrt(a^22a+1+b^2)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Now I am going to square both sides again

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[(4a 16)^2 = 64((a1)^2 + b^2)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Finally we have no more square roots

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Now i am going to expand

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[16a^2 128a + 256 = 64 a^2 128a + 64 + 64b^2)\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it ends up as 192=48a^2+64b^2 I think

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Final step: complete the square on a term

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry yeah that was the answer 192 = 48a^2 +64b^2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0And thats an eclipse.
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