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9709 P3 - Nov 2003 - Q7
1915

The complex number u is given by \(u = \frac{7 + 4i}{3 - 2i}\).

  1. Express u in the form \(x + iy\), where x and y are real.
  2. Sketch an Argand diagram showing the point representing the complex number u. Show on the same diagram the locus of the complex number z such that \(|z - u| = 2\).
  3. Find the greatest value of \(\arg z\) for points on this locus.
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