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henpen
 2 years ago
A complex question
henpen
 2 years ago
A complex question

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henpen
 2 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.

henpen
 2 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)

henpen
 2 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?

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1 a + bi  1 + a + bi + 1 = 4

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

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

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Then you should square both sides

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Actually that will be hard

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1So move one of the square roots on the left then square both sides

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Which will give you this

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

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1I will get rid of it soon

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Ok now i am going to cancel some stuff and simplify this equation

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Now i can simplify further

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

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Now I am going to square both sides again

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Finally we have no more square roots

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Now i am going to expand

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

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

henpen
 2 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!

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1Final step: complete the square on a term

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

baddinlol
 2 years ago
Best ResponseYou've already chosen the best response.1And thats an eclipse.
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