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Urgent help needed with complex numbers 
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#1
Jun508, 10:31 PM

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1. The problem statement, all variables and given/known data
a complex no. z is represented by the point T in an Argand diagram. [tex]z=\frac{1}{3+it}[/tex] where t is a variable show that z+z*=6ZZ* and that as t varies,T lies on a circle, and state its centre 2. Relevant equations 3. The attempt at a solution Did the first part easily. Need help with the 2nd part with the circle so far I multiplied z by z*/z* to get [tex]z=\frac{3it}{p+t^2}[/tex] Do I now say that let z=x+iy and then find z and the modulus of the otherside (with t) and put that in the form [itex]x^2+y^2+2fx+2gy+c=0[/itex] ? 


#2
Jun508, 10:53 PM

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p is 9, right? Sure, you now have x=3/(9+t^2) and y=(t)/(9+t^2). Eliminate the t in favor of x and y and write the quadratic form.



#3
Jun508, 11:06 PM

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so then [tex]y^2=\frac{t^2}{9+t^2}[/tex] and from the eq'n in x [tex]t^2=\frac{3}{x}9[/tex] making [tex]y^2=(\frac{3}{x}9)(\frac{x^2}{9})[/tex] [tex]x^2+y^2\frac{1}{3}x=0[/tex] correct? 


#4
Jun508, 11:11 PM

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Urgent help needed with complex numbers
Small error here: Wasn't y = t/(9+t^2) ? You didnt square denominator.



#5
Jun508, 11:14 PM

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I did,I just left it out when typing
x^2/9 is 1/(9+t^2)^2 


#6
Jun508, 11:16 PM

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y^2=t^2/(9+t^2)^2. But everything else is correct, so I'll take that as a typo. Ok, so what's the center and radius?



#7
Jun508, 11:21 PM

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then centre will just be (1/6,0) and the radius is 1/6



#8
Jun508, 11:26 PM

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Yeah, Defennder is on your tail so you are rushing it right? Don't. You have a sign error in the center. Fix it quick! If y=0 then x=0 and x=1/3 are both on the curve.



#9
Jun508, 11:31 PM

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[tex] x^2+y^2\frac{1}{3}x=0 [/tex]
[tex] x^2+y^2+2(\frac{1}{6}x)+2(0)+0=0[/tex] f=1/6 g=0 c=0 is the eq'n wrong or did I actually not sq. the denominator? 


#10
Jun508, 11:36 PM

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What are you doing? Just complete the square. x^22(x/6)=(x1/6)^2(1/6)^2. x1/6 not x+1/6.



#11
Jun508, 11:41 PM

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ahhh....my brain is idle
when put in the form [itex]x^2+y^2+2fx+2gy+c=0[/itex] ,the centre is (f,g) sorry about my mistake so the centre is (1/6,0) and radius is 1/6 


#12
Jun508, 11:44 PM

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No need to apologize. But, that's the problem with trying to memorize too many formulas you don't need.



#13
Jun508, 11:46 PM

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yeah,I know but when I learnt the equation of a circle, that equation was the one I remembered more than the other one.
But anyhow,thanks!! 


#14
Jun508, 11:48 PM

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