**Finding Locus of Complex Numbers Practice Worksheet :**

Here we are going to see some example problems finding locus of complex numbers practice worksheet.

(1) If z = x + iy is a complex number such that |(z - 4i)/(z + 4i)| = 1 show that the locus of z is real axis. Solution

(2) If z = x + iy is a complex number such that im (2z + 1)/(iz + 1) = 0, show that locus of z is 2x^{2} + 2y^{2} + x - 2y = 0 Solution

(3) Obtain the Cartesian form of the locus of z = x + iy in each of the following cases:

(i) [Re (iz)]^{2} = 3

(ii) im [(1 - i)z + 1] = 0

(iii) |z + i| = |z - 1|

(iv) z bar = z^{-1 }Solution

(4) Show that the following equations represent a circle, and, find its centre and radius

(i) |z - 2 - i| = 3

(ii) |2z + 2 − 4i| = 2

(iii) |3z − 6 +12i| = 8. Solution

(5) Obtain the Cartesian equation for the locus of z = x + iy in each of the following cases:

(i) |z − 4| = 16

(ii) |z − 4|^{2} - |z - 1|^{2} = 16 Solution

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