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

The set {R e((2i z)/(1-z^2)): z is a comp l e x n u mber ,|z|=1,z=+-1} is________.

The set {R e((2i z)/(1-z^2)): z is a complex number , |z|=1,z=+-1} is________.

The set {R e((2i z)/(1-z^2)): z is a complex number ,|z|=1,z=+-1} is________.

The set {R e((2i z)/(1-z^2)): z is a complex number, |z|=1,z=+-1} is________.

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

If z=1+i , then the argument of z^(2)e^(z-i) is

A relation R on the set of complex number is defined by z_1 R z_2 iff (z_1 - z_2)/(z_1+z_2) is real ,show that R is an equivalence relation.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and only if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.

A relation R on the set of complex numbers is defined by z_1 R z_2 if and oly if (z_1-z_2)/(z_1+z_2) is real Show that R is an equivalence relation.