mathematics(complex)

Question

If the center of the regular hexagon is at origin and one of the vertex on argand diagram is 1+2i, then the perimeter is?

Answer 1

A regular hexagon is made up of 6 equilateral triangles.  Thus the distance from the center to any vertex is equal to the length of an external side.

 

The center is located at (0,0) and one vertex is located at (1,2).  The radial distance from the origin to the vertex can be determined from the Pythagorean Theorem:

 

r = √(1²+2²) = √5

 

A regular hexagon has six equal sides.  In this case, each side's length is √5.  The perimeter, then is:

 

Perimeter = 6√5