IIT JEE , AIEEE Forum - Mathematics , Algebra - complex no.....equilateral triangle........

nayan_dbb

z1 = 1/2 ( 1 + (3^(1/2) i) )
z2 = - 1
and z3 form an equilateral triangle then z3 is

a) -pi/3
b) -pi/2
c) -2 pi/3
d)None of these

spt_001

all the 3 vertices lie on mod(z)=1 the centroid is (0,0)

karthik2007

For an equilateral triangle,
z1^2 + z2^2 + z3^2 = z1z2 + z2z3 + z3z1

Use this relation to find the unknown.

sudeep.kumar

Draw the argand diagram ..

the two given vertices are (-1,0) and (1/2, root3/2).... so the two position vectors will be at angle 60 and 180 with positive x axis.. hence the third vector must be directed at -60 degree with the positive x axis, so that the three vectors are at 120 degree with each other and hence form a equilateral triangle...

while solving objective question, always try to draw the diagram if you can... there may be some simple shortcut for the problem.

shubhayan_c

I agree with sudeep always try to visuallize the problem then it will become much easier to solve

pottermania1990

when r the results of quick silver test comin...im waitin mann

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