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anonymous
 5 years ago
write quotient in standard form 9+5i / 69i
anonymous
 5 years ago
write quotient in standard form 9+5i / 69i

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0multiply both the top and the bottom by the conjugate of the denominator. The conjugate of a+bi = abi. Do that and see what happens to the denominator. :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw, the standard form is a+bi

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.06+9i. b in this case would be 9 so the conjugate is 6(9)i which is equal to 6+9i

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0whenever you want to get rid of the imaginary part of a complex denominator, multiply the top and bottom by the conjugate of the denominator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.09+5i * 6+9i ? 69i * 6+9i ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I assume that the first line is the numerator and the second line is the denominator?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.054 + 45i ? 36 + 81i ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes first line is the numerator and the second line is the denominator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Ok, you got the denominator right but (9+5i)*(6+9i) = 54 + 81i + 30i + 45

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0wait, sorry. the denominator is wrong too. it is 36+81

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i^2 = 1 because i = \[\sqrt{1}\] so i^2 = \[\sqrt{1}\] * \[\sqrt{1}\] = 1

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0agh sorry about not having it in one line

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0its okay (: , im just trying to understand it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you understand how i^2 is 1?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so i would have to add the top and it'll be 99 + 111i ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that it will result to the opposite ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(9+5i) / (69i) = [(9+5i)(6+9i)] / [(69i)(6+9i)]\] Then multiply it out. Remember that (a+b)(c+d) = ac + ad + bc + bd

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So \[(9+5i)(6+9i) = 9*6 + 9*9i + 6*5i + 5*9*i^2\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.05*9*i^2 = 1*5*9. Just do the same thing for the denominator, too.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so its not (9+5i)*(6+9i) = 54 + 81i + 30i + 45 ?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0suppose x+yi(x，y∈R)，satisfies (9+5i)÷(69i)=a+bi , then (x+yi)*(69i)=9+5i. we must remember the logarithm of imaginaries as: (a+bi)(c+di)=(ac－bd)+(bc+ad)i. then 6x+9y=9, 6y9x=5. so x=1/13, y=37/39. so 9+5i / 69i = 1/13 + 37/39 i

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That's right kathy. So in standard form it is (54+45) + (81+30)i = 99+111i Now try doing the denominator. Something interesting should happen.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0my method is a traditional one. Johnfreeman uses the idea of rationalization.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yes thats the answer they give here as an option :) so to solve problems with i i would have to use logarithm of imaginaries?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I think the easiest way to think of it at this point is to multiply the top and bottom by the conjugate because then you get a rational denominator.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It should at least be good practice to try multiplying the denominator by its conjugate so you know what happens when you do that. It is probably how they want you to solve this anyway.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0clear, you can use tthe data in the problem to directly work it out: 9+5i / 69i=[9*6+5*(9)]/[6^2+(9)^2] + [5*69*(9)]/[6^2+(9)^2]*i = 1/13 + 37/39 i

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0see, the answer's just the same.
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