IV. ROOTS OF COMPLEX NUMBERS

1. Find and plot on the complex plane the values of z for which :

(a) (b) (c)

(d) (e) (f)

(h) (i)

2. Find

(a) the fifth root of 32. (b) the square root of 3+4i

(c) the square root of 7-24i (d) the fourth roots of 8.

(e) the fifth roots of i (f) the cube root of

(g) (h) the square root of 8-6i

3. Three points, of which is one point, lie on the circumference of a circle of radius 2 units and centre at the origin. If these three points form vertices of an equilateral triangle, find the other two points.

4. If 1, , are the cube root of unity, prove that

(a)

(b)

(c)