" Let "z in C" be such that "|z|<1" .If "omega=(5+3z)/(5(1-z))" ,then:- "

Let z in C be such that Re(z^(2)) = 0 , then

Let S={ Z in C : | z - 1|=1 and (sqrt 2 - 1) (z overline z) - i(z - overline z) = 2 sqrt 2} . Let z_1, z_2 be such that |z_1| = max_(z in S) |z| and |z_2| = min_(z in S) |z| . Then |sqrt2 z_1 - z_2|^2 equals:

Let z_(1),z_(2)in C such that z_(1)^(2)+Z_(2)^(2)in R. If z_(1)(z_(1)^(2)-3z_(2)^(2))=10 and z_(2)(3z_(1)^(2)-z_(2)^(2))=30 Find the value of (z_(1)^(2)+z_(2)^(2))

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z and w are two non zero complex number such that |z|=|w|, and Arg(z)+Arg(w)=pi then (a) z=w (b) z=overlinew (c) overlinez=overlinew (d) overlinez=-overlinew

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

Let z_(1),z_(2) be two complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| . Then,

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