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livelaughlilz
 3 years ago
express sqrt(53i) in the a+bi form
livelaughlilz
 3 years ago
express sqrt(53i) in the a+bi form

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

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

livelaughlilz
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0Yes.It's Wrong.I Forgot....sorry

livelaughlilz
 3 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
 3 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
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.0yes i just checked i have the right problem

phi
 3 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
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1the ± give you different answers. (square roots will have 2 answers)

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

livelaughlilz
 3 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
 3 years ago
Best ResponseYou've already chosen the best response.1remember you can use wolfram to check your answers
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