Question

What is the distance on the unit circle between successive fourth roots of StartFraction StartRoot 3 EndRoot Over 2 EndFraction minus one-half I ?

a) pi/3

b) pi/2

c) 2pi/3

d) pi

Answer 1

The distance between successive fourth roots of √3/2 - (1/2)i on the unit circle is π/2.

Step-by-step explanation:

To find the distance between successive fourth roots of √3/2 - (1/2)i on the unit circle, we need to determine the angle between these points. We can use the polar form of a complex number to represent the given expression as 1(cos(210°) + isin(210°)). Since the unit circle is divided into 360°, the angle between successive roots is 360°/4 = 90°. Therefore, the distance between successive fourth roots is 90° = π/2.

Answer 2

The answer is B. pi/2