IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: aparna.agrawal1995 on October 26, 2011, 01:51:00 pm

Title: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 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.

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha on October 26, 2011, 02:31:29 pm

1

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha on October 26, 2011, 04:46:34 pm

Sorry, there was a problem with my browser...

Title: Re: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 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?

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha 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. :)

Title: Re: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 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?

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha 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. :)

Title: Re: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 on October 26, 2011, 05:51:03 pm

Ohhh..thanks. By the way are you given any exams currently?

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha 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.

Title: Re: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 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?

Title: Re: Urgent Complex Numbers Doubts
Post by: Alpha 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.:)

Title: Re: Urgent Complex Numbers Doubts
Post by: aparna.agrawal1995 on October 26, 2011, 06:00:00 pm

Good night. Take care. :)