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Urgent Complex Numbers Doubts

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aparna.agrawal1995:
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.

Alpha:
1

Alpha:
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aparna.agrawal1995:
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?

Alpha:
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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