Questions
Let and be two non-zero complex numbers such that then the origin and points represented by and
a
lie on a straight line
b
form a right triangle
c
form an equilateral triangle
d
none of these
detailed solution
Correct option is C
Let z=z1z2, and z+1z=1⇒ z2-z+1=0⇒ z=1±3i2 ⇒ z1z2=1±3i2If z1 and z2 are represented by A and B respectively and O be the origin, thenOAOB=z1z2=1±3i2=14+34=1⇒ OA=OBAlso, ABOB=z2−z1z2=1−z1z2 =1−12±32i=12∓32i=14+34=1⇒ AB=OBThus, OA=OB=AB.∴ ∆OAB is an equilateral triangle.Talk to our academic expert!
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The complex number z, satisfies the condition The maximum distance from the origin of coordinates to the point is
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