N2011 P2 Q1
N2011 P2 Q1
Junior College 2
8 marks
The complex number \(z\) satisfies \(|z-2-5\mathrm i|\le3\).
- On an Argand diagram, sketch the region in which the point representing \(z\) can lie.[3]
- Find exactly the maximum and minimum possible values of \(|z|\).[2]
- It is given that \(0\le\arg z\le\frac14\pi\). With this extra information, find the maximum value of \(|z-6-\mathrm i|\). Label the point(s) that correspond to this maximum value on your diagram with the letter \(P\).[3]
Solution:
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Answer:(ii) Maximum \(\sqrt{29}+3\), minimum \(\sqrt{29}-3\). (iii) \(\sqrt{17}\), at \(z=2+2\mathrm i\) and \(z=5+5\mathrm i\).
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