1Ya, such prob can be solved with simple geom, as Nishant sir said......
A(z1), B(z2), C(z3), D(z4), E(z5) are the vertices of a regular polygon ABCDE in anti clockwise order whose centre is at the origin O and M(z) is point inside the polygon.
1) If |arg(z4-z5/z-z5)| = |arg(z-z3/z4-z3)| = θ then range of θ for which there exists two such M(z) is
A) [ 0,3Î /5) B) [0,Ï€/5)
c) (0,2Ï€/5) d) none of these
2) If arg(z4-z5/Z-Z5) = arg(z-z3/z4-z3) = 7∩/30 , then the value of arg(z5-Z1/z-z1) is equal to
A) ∩/4 B) 7∩/30
C) 4∩/15 D) ∩/3
3) The value of arg (z2-z)/(z1-z) in the previous condition is
(A) pi/4
(B) 7pi/30
(C) 4 pi / 15
(D) pi/3
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3 Answers
62Hint for this one..
Draw a regular polygon and see what each of the || or arguments mean.. They mean the angle between two lines...
Now you need two solutions to these..
What range of the angle will satisfy?
You wont need any complex numbers but simple geometry..
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