(1)z=1+cos((10 pi)/(9))+i sin((10 pi)/(9))

Find the modulus,argument and the principal argument of the complex numbers: a z=1+cos((10 pi)/(9))+i sin((10 pi)/(9))(b)z=-2(cos30^(@)+i sin30^(@))

The principal value of the arg(z) and lzl of the complex number z=1+cos((11 pi)/(9))+i sin((11 pi)/(9)) are respectively

If z_(k)=cos((k pi)/(10))+i sin((k pi)/(10)), then z_(1)z_(2)z_(3)z_(4) is equal to (A)-1 (B) 2(C)-2 (D) 1

Let quad cos(2k(pi)/(10))+i sin(2k(pi)/(10));k=1,2,34,...,9z_(k)=cos(2k(pi)/(10))+i sin(2k(pi)/(10));k=1,2,34,...,9 (A) For each z_(k) there exists a z_(j) such that z_(k).z_(j)=1 (ii) there exists a k in{1,2,3,...,9} such that z_(1)z=z_(k)

Find the incentre of a triangle formed by the lines x "cos" (pi)/(9) + y "sin" (pi)/(9) = pi, x "cos" (8pi)/(9)+ y "sin" (8pi)/(9) = pi " and x "cos" (13pi)/(9) + y "sin" ((13pi)/(9)) = pi.

Find the incentre of a triangle formed by the lines x "cos" (pi)/(9) + y "sin" (pi)/(9) = pi, x "cos" (8pi)/(9)+ y "sin" (8pi)/(9) = pi " and x "cos" (13pi)/(9) + y "sin" ((13pi)/(9)) = pi.

The value of (1+cos((pi)/(9)))(1+cos((3 pi)/(9)))(1+cos((5 pi)/(9)))(1+cos((7 pi)/(9)))

The sum cos ((pi) / (9)) + cos ((2 pi) / (9)) + cos ((3 pi) / (9)) + ... + cos ((17 pi) / (9 )) =

Prove that: sin((4 pi)/(9)+7)cos((pi)/(9)+7)-cos((4 pi)/(9)+7)sin((pi)/(9)+7)=(sqrt(3))/(2)