complex nos (1 Viewer)

[kevin101]

help with this question

Three points, of which 1+i root3 is one point, lie on the circumference of a circle of radius 2 units and centre at the origin. If these points form the vertices of an equilateral triangle, find the other two points.

(ANS: -1, 1-i root3)

thanks and working pls

 

[kevin101]

hmm i got something different.

seeing as the points form a triangle the angle from 1+iroot3 to each of the the other points must be 120. as 120+120+120=360 a revolution

i let point B = to 1+i root3
A and C are other two points lying on circle. and O is origin

so OB rotated cis120 = OA
1+i root3 times cis120 = a
(1+ i root3)(-1/2 + root3/2 i) = a
expand and you'll get a=-2, your first point

then OB rotated cis-120 = OC
(1+root3 i) times cis-120 = c
(1+root3 i)(-1/2 - root3/2 i) = c
expand and c = 1- root3 i

so my two points are -2 and 1- root3 i

im pretty sure this is right

 

[khorne]

@ Kevin101, yes that is right