Q.11 Let Z be a complex number of maximum amplitude satisfying (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.
(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.