Z is a complex number such that Z ≤ 2 and - π 3 ≤ amp Z ≤ π 3 . The area of the region formed by locus of Z is (in sq. units)

Step-by-step solution

Given Z ≤ 2 and - π 3 ≤ amp Z ≤ π 3 . This represents a sector of a circle of whose radius is less than or equal to 2 units with the central angle equal to 2 π 3 . From the above diagram, the locus of Z will form a sector O A B O . Thus, the area of the region formed by locus of Z = Area of the sector O A B O = 1 2 × radius 2 × central angle = 1 2 × 2 2 × 2 π 3 sq. units = 4 π 3 sq. units