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 2x² + 2y² + 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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