Show that `a=r omega^(2)`.

Show that v=r omega .

If |z| <= 1 and |omega| <= 1, show that |z-omega|^2 <= (|z|-|omega|)^2+(arg z-arg omega)^2

A thin circular loop of radius R rotates about its vertical diameter with an angular frequency omega . Show that a small bead on the wire loop rem ains at its lowermost point for omega oversetlarrsqrt(g/R) What is the angle made by the radius vector joining the centre to the bead with the vertical downward direction for omega = sqrt (2g/R) ? neglect friction.

Sum the series : 1(2-omega)(2-omega^(2))+2(3-omega)(3-omega^(2))......(n-1)(n-omega)(n-omega^(2)) where omega and omega^(2) are non-real cube roots of unity.

Let omega be a complex cube root of unity with omega ne 1 . A fair die is thrown three times. If r_(1), r_(2) and r_(3) are the numbers obtained on the die, then the probability that omega^(r_(1)) + omega^(r_(2)) + omega^(r_(3)) = 0 is

Show that the polynomial x^(4p)+x^(4q+1)+x^(4r+2)+x^(4s+3) is divisible by x^3+x^2+x+1, w h e r ep ,q ,r ,s in ndot

Show that 16R^(2)r r_(1) r _(2) r_(3)=a^(2) b ^(2) c ^(2)

Show that r_(1)+r_(2)=c cot ((C)/(2))

In a DeltaABC, show that r_(1)* r_(2)* r_(3)*r=Delta^(2).

Show that for a spherical convex mirror f=R/2 .