Q.11 Let Z be a complex number of maximum amplitude satisfying  Z - 3   =   R e ( z )     ,   t h e n   Z - 3   i s   e q u a l   (a) 1  (b) 2 (c) 3   (d) 9 

If the magnitude of z-3 is equal to the real part of z, then z could be 1.5 + 0i, or, what else? Two other possibilities are z = 3 +/- 3i. To find some other solutions I could set 
(x-3)^2 + y^2 = x^2 => 6x - 9 = y^2, 
yielding solutions such as z = 13/6 +/- 2i. 

The amplitude of z will be greatest at (3,3), where |z - 3| = |3i| = 3, so m = 3.

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