and 
are nonzero complex numbers such that 
and 
, then which of the following statements is/are true?
, then 
, and 
are collinear and 
, 
are collinear separately. 
are complex numbers, where 
, then triangles formed by points 
and 
are similar. 
are distinct complex numbers, then points 
, 
and 
are not connected by any well defined geometry. 
, then 
divides the line joining 
and 
internally and if 
, then 
divides the line joining of 
externally.
Text Solution
Verified by ExpertsD
(a, b, c, d)
Hence, 
divides the line joining 
and 
in the ratio 
. That means the given points are collinear. Also, the ratio 
(or 
) if 
divides the line joining 
and 
internally and 
(or 
or 
) if 
divides the line joining 
externally.
When 
are complex numbers, where 
, we have 
and 
.
Comparing the value of 
, we have
Hence, triangles 
and 
are similar.
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