A community for students.
Here's the question you clicked on:
 0 viewing
livelaughlilz
 2 years ago
express sqrt(53i) in the a+bi form
livelaughlilz
 2 years ago
express sqrt(53i) in the a+bi form

This Question is Closed

phi
 2 years ago
Best ResponseYou've already chosen the best response.1you could try using \[ (a+bi)^2 = 53i \] this means \[ a^2b^2 + 2abi = 5 3i\] equate real with real, and imag with imag. solve for a and b

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0by equate do you mean say a2^b2 = 5 and 2abi = 3i? as in set up two seperate equations?

FaisalAyaz
 2 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{53i} = \sqrt{5}  \sqrt{3i}\]

phi
 2 years ago
Best ResponseYou've already chosen the best response.1a^2  b^2 = 5 and 2abi = 3i yes

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0@FaisalAyaz i don't think it does. \[\sqrt{a + b} \neq \sqrt{a}+\sqrt{b}\]

FaisalAyaz
 2 years ago
Best ResponseYou've already chosen the best response.0Yes.It's Wrong.I Forgot....sorry

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0@phi for the a^2  b^2 = 5 part i got a = +/ 3, and b = +/2 (by guess and check, i'm not sure how to do it algebraically) for the 2abi = 3i i got ab = 3/2 i'm slightly stuck. do i try and solve a system of equations now since i have two equations, or somehow plug the values back in, or what?

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0@phi i got 32i and 3+2i as my answers. is that right?

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0then is it wrong that a and b are (3, 2) or (3, 2)?

phi
 2 years ago
Best ResponseYou've already chosen the best response.1I am getting some very ugly numbers for this problem. see http://www.wolframalpha.com/input/?i=%28sqrt%28+0.5%285%2Bsqrt%2834%29%29%293%2F%282*sqrt%28+0.5%285%2Bsqrt%2834%29%29%29%29*i%29%5E2 Are you sure you have the correct problem?

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0yes i just checked i have the right problem

phi
 2 years ago
Best ResponseYou've already chosen the best response.1you can get the ugly result by saying 2ab= 3 b= 3/(2a) b^2 = 9/(4a^2) sub into a^2  b^2 =5 a^2  9/(4a^2) = 5 multiply by 4a^2 4a^4 20a^2 9 =0 or a^4 5a^2 9/4  0 let x= a^2, so you get a quadratic x^2  5x 9/4=0 use the quadratic formula to find x. then take the square root of x to find a then solve for b

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0what bout the plus or minus part? i have [5 +/ sqrt(34)]/[2]  b^2 = 5

phi
 2 years ago
Best ResponseYou've already chosen the best response.1the ± give you different answers. (square roots will have 2 answers)

phi
 2 years ago
Best ResponseYou've already chosen the best response.1first choose + and find the answers then 

livelaughlilz
 2 years ago
Best ResponseYou've already chosen the best response.0okay. i have to go now. i might sign on later, after i work on the problem some more. thank you. bye.

phi
 2 years ago
Best ResponseYou've already chosen the best response.1remember you can use wolfram to check your answers
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.