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Author Topic: Urgent Complex Numbers Doubts  (Read 2445 times)

Offline aparna.agrawal1995

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Urgent Complex Numbers Doubts
« on: October 26, 2011, 01:51:00 pm »
Q. The complex number u is de?ned by u = (6?3i)/(1+2i)

For complex numbers z satisfying arg(z?u) =(1/4)pie, ?nd the least possible value of |z|. [3]

=> When rationalised, u comes out to be -3i

I have a problem solving the question further those i have attempted the other parts to the question. This question is from 2011 M/J V1 (A levels).
Please help me with this question. I have an exam day after tomorrow.
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #1 on: October 26, 2011, 02:31:29 pm »
1
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #2 on: October 26, 2011, 04:46:34 pm »
Sorry, there was a problem with my browser...
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Offline aparna.agrawal1995

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Re: Urgent Complex Numbers Doubts
« Reply #3 on: October 26, 2011, 04:54:43 pm »
Thank you so much.  :)
I just want to know one more thing. If the question was to switched to the greatest possible value then the answer would be 3 units?
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #4 on: October 26, 2011, 05:05:44 pm »
Isn't it already greatest possible value?

If you meant the least value, it would be distance OC. z moves round the circle. From the origin, C is the point where its distance is least.
OC= root of 18-1, i.e. OA- AC.

You're welcome. :)
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Offline aparna.agrawal1995

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Re: Urgent Complex Numbers Doubts
« Reply #5 on: October 26, 2011, 05:26:43 pm »
Nope. I'm talking about the 2nd part only. The question asks for the least value of |z| when the arg(z-u) = pie/4. Now if the question is switched to asking the greatest value of |z| when the arg(z-u) = pie/4, then how would i do it?
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #6 on: October 26, 2011, 05:41:14 pm »
No, it cannot ask you that. Else, it'll extend till infinity, unless there's some limit given. Notice the half-line ends with an arrow, implying it stretches till infinity. :)
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Offline aparna.agrawal1995

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Re: Urgent Complex Numbers Doubts
« Reply #7 on: October 26, 2011, 05:51:03 pm »
Ohhh..thanks. By the way are you given any exams currently?
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #8 on: October 26, 2011, 05:53:21 pm »
I was waiting for your reply. :)

Yes, the same Maths P3 you'll give on Friday. ::)

Welcome, by the way.
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Offline aparna.agrawal1995

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Re: Urgent Complex Numbers Doubts
« Reply #9 on: October 26, 2011, 05:57:06 pm »
All the best then. :) I have my english language commentary paper too tomorrow. :( People here are celebrating Diwali and I'm stuck studying for my exams. Its so irritating. :/
By the way, you take english language?
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Alpha

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Re: Urgent Complex Numbers Doubts
« Reply #10 on: October 26, 2011, 05:58:38 pm »
Thanks, and same to you. :)

Yeah, for Eid too. :(

Nah, I take General Paper. Anyway, gotta go now. Good night.:)
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Offline aparna.agrawal1995

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Re: Urgent Complex Numbers Doubts
« Reply #11 on: October 26, 2011, 06:00:00 pm »
Good night. Take care. :)
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