Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

henpen Group TitleBest 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.
 2 years ago

henpen Group TitleBest ResponseYou've already chosen the best response.0
(Where z=a+ib)
 2 years ago

henpen Group TitleBest ResponseYou've already chosen the best response.0
(And by 'graphically' I mean plotting the possible values of z on the complex plane)
 2 years ago

henpen Group TitleBest 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?
 2 years ago

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

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

baddinlol Group TitleBest 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)
 2 years ago

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

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

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

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

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

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

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

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

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

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

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

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

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

henpen Group TitleBest ResponseYou've already chosen the best response.0
4a16=8sqrt(a^22a+1+b^2)
 2 years ago

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

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

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

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

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

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

baddinlol Group TitleBest ResponseYou've already chosen the best response.1
Now simlify...
 2 years ago

baddinlol Group TitleBest ResponseYou've already chosen the best response.1
SSo you get
 2 years ago

henpen Group TitleBest 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!
 2 years ago

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

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

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

baddinlol Group TitleBest ResponseYou've already chosen the best response.1
No problem. =)
 2 years ago
See more questions >>>
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.