A community for students.
Here's the question you clicked on:
 0 viewing
henpen
 3 years ago
A complex question
henpen
 3 years ago
A complex question

This Question is Closed

henpen
 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.

henpen
 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)

henpen
 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?

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

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

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

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

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

baddinlol
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1Which will give you this

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

baddinlol
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1I will get rid of it soon

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

baddinlol
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1Now i can simplify further

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

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

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

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

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

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

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

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

henpen
 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!

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

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

baddinlol
 3 years ago
Best ResponseYou've already chosen the best response.1And thats an eclipse.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.