The set `{R e((2i z)/(1-z^2)): zi sacom p l e xnu m b e r ,|z|=1,z=+-1}` is________.

Let z_(1)=e^((i pi)/(5))

If zis a complex number,then |3z-1|=3|z-2| represents

if z_(1) = 3i and z_(2) =1 + 2i , then find z_(1)z_(2) -z_(1)

Let z be not a real number such that (1+z+z^(2))/(1-z+z^(2))in R, then prove tha |z|=1

Let theta_1 , theta_2 , … , theta_(10) be positive valued angles (in radian) such that theta_1+theta_2+ … +theta_(10)=2pi . Define the complex numbers z_1=e^(itheta_(1)) ,z_k= z_(k-1)e^(itheta_(k)) for k = 2, 3, … , 10 , where i = sqrt(−1) . Consider the statements ? and ? given below: P:abs(z_2-z_1)+abs(z_3-z_2)+ . . . +abs(z_(10)-z_9)+abs(z_1-z_(10)) le 2pi Q:abs(z_2^2-z_1^2)+abs(z_3^2-z_2^2)+ . . . +abs(z_(10)^2-z_9^2)+abs(z_1^2-z_(10)^2) le 4pi Then

Let z=a+ib=re^(i theta) where a, b, theta in R and i=sqrt(-1) Then r=sqrt((a^(2)+b^(2)))=|Z| and theta=tan^(-1)((b)/(a))=arg(z) Now |z|^(2)=a^(2)+b^(2)=(a+ib)(a-ib)=zbar(z) rArr(1)/(2)=(bar(z))/(|z|^(2)) and |z_(1)z_(2)z_(3)......z_(n)|=|z_(1)||z_(2)||z_(3)|...|z_(n)| If |f(z)|=1 ,then f(z) is called unimodular. In this case f(z) can always be expressed as f(z)=e^(i alpha), alpha in R Also e^(i alpha)+e^(i beta)=e^(i((alpha+beta)/(2)))*2cos((alpha-beta)/(2)) and e^(i alpha)-e^(i beta)=e^(i((alpha+beta)/(2)))*2i sin((alpha-beta)/(2)) where alpha, beta in R Q:If Z_(1),Z_(2),Z_(3) are complex number such that |Z_(1)|=|Z_(2)|=|Z_(3)|=|Z_(1)+Z_(2)+Z_(3)|=1 , then |(1)/(Z_(1))+(1)/(Z_(2))+(1)/(Z_(3))| is

Let R be the relation defined on set of all complex numbers C as z_(1)Rz_(2) hArr |z_(1)|=|z_(2)| then 'R' is -

If a,b in R and z_(1),z_(2) are complex numbers such that |(az_(1)-bz_(2))/(ab-z_(1)bar(z)_(2))|=1 and |z_(2)|!=a then find |z_(1)|.]|

Let'a = (z + 2)(2 + 2i) is purely real and a e[-1, 2] where z is a complex number and z = x + jy(x, y E R), then -(1) 12/max = 6(2) z/mex = 2+2(3) Iz/min = V3(4) [z/min = 0