1. LOCUS IN THE COMPLEX PLANE The locus defines the path of a complex number Recall from the start of the chapter that the modulus and the argument defines the position of a ‘z’ Also recall that the equation of a circle with radius ‘r’ and centre (a,b)

2. The complex number z moves in the complex plane subject to the condition Find the equation of the locus of z and interpret the locus geometrically. The locus of the complex number ‘z’ is therefore the points on the circle centre the origin and radius r = 9

3. The complex number z moves in the complex plane subject to the condition. Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the set of points on the circumference of the circle with centre (1, 2) and radius 4.

4. The complex number z moves in the complex plane subject to the condition Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the set of points which lie inside the circle with centre (0, 1) and radius 2. [Note that if the condition was the locus of z would be the set of points which lie on or inside the circle with centre O and radius 2.]

5. The complex number z moves in the complex plane subject to the condition. Find the equation of the locus of z and interpret the locus geometrically. The locus of z is the straight line.

6. The complex number z moves in the complex plane such that Show that the locus of z is a straight line and find the equation of the locus of z. The equation of the locus of z is