Let `za n dw` be two nonzero complex numbers such that `|z|=|w|a n d arg(z)+a r g(w)=pidot` Then prove that `z=- bar w dot`

If z_1a n dz_2 are two complex numbers such that |z_1|=|z_2|a n d arg(z_1)+a r g(z_2)=pi , then show that z_1,=-( barz )_2dot

z and omega are two nonzero complex number such that |z|=|omega|" and "Argz+Arg omega= pi then z equals

If z and omega are two non-zero complex numbers such that |z omega|=1" and "arg(z)-arg(omega)=(pi)/(2) , then bar(z)omega is equal to

Let z be any non zero complex number then arg z + arg barz =

If z_1a n dz_2 are two nonzero complex numbers such that = |z_1+z_2|=|z_1|+|z_2|, then a rgz_1-a r g z_2 is equal to -pi b. pi/2 c. 0 d. pi/2 e. pi

Let z, omega be complex numbers such that bar(z)+ibar(omega)=0" and "arg z omega= pi . Then arg z equals

Let z and omega be two complex numbers such that |z|lt=1,|omega|lt=1 and |z-iomega|=|z-i bar omega|=2, then z equals (a) 1ori (b). ior-i (c). 1or-1 (d). ior-1

If z_1, z_2, z_3 are three nonzero complex numbers such that z_3=(1-lambda)z_1+lambdaz_2w h e r elambda in R-{0}, then prove that points corresponding to z_1, z_2a n dz_3 are collinear .

Let a ,b ,a n dc be any three nonzero complex number. If |z|=1a n d' z ' satisfies the equation a z^2+b z+c=0, prove that a ( bara) =c (barc) a n d|a||b|=sqrt(a c( bar b )^2)

If z_(1)" and "z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_1|+|z_(2)| , then arg z_(1)- arg z_(2) is equal to