If`z_(1),z_(2)inC,z_(1)^(2)+z_(2)^(2)inR,z_(1)(z_(1)^(2)-3z_(2)^(2))=2` and `z_(2)(3z_(1)^(2)-z_(2)^(2))=11,` the value of `z_(1)^(2)+z_(2)^(2)` is

If z_(1),z_(2)in C,z_(1)^(2)in R,z_(1)(z_(1)^(2)-3z_(2)^(2))=2 and z_(2)(3z_(1)^(2)-z_(2)^(2))=11 ,then the value of z_(1)^(2)+z_(2)^(2) is 10 b.12 c.5d.8

z_(1),z_(2)in c and z_(1)^(2)+z_(2)^(2)in Rz_(1)(z_(1)^(2)-3z_(2)^(2))=2,z_(2)(3z_(1)^(2)-z_(2)^(2))=11 If z_(1)^(2)+z_(2)^(2)=lambda then determine lambda^(2)

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))

If z_(1),z_(2)inC , show that (z_(1)+z_(2))^(2)=z_(1)^(2)+2z_(1)z_(2)+z_(2)^(2) .

If z_(1) and z_(2) are two complex numbers,then (A) 2(|z|^(2)+|z_(2)|^(2)) = |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2) (B) |z_(1)+sqrt(z_(1)^(2)-z_(2)^(2))|+|z_(1)-sqrt(z_(1)^(2)-z_(2)^(2))| = |z_(1)+z_(2)|+|z_(1)-z_(2)| (C) |(z_(1)+z_(2))/(2)+sqrt(z_(1)z_(2))|+|(z_(1)+z_(2))/(2)-sqrt(z_(1)z_(2))|=|z_(1)|+|z_(2)| (D) |z_(1)+z_(2)|^(2)-|z_(1)-z_(2)|^(2) = 2(z_(1)bar(z)_(2)+bar(z)_(1)z_(2))

If z_(1) + z_(2) + z_(3) = 0 and |z_(1)| = |z_(2)| = |z_(3)| = 1 , then value of z_(1)^(2) + z_(2)^(2) + z_(3)^(2) equals

Let z_(0) be the circumcenter of an equilateral triangle whose affixes are z_(1),z_(2),z_(3) . Statement-1 : z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=3z_(0)^(2) Statement-2: z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=2(z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1))

If |z_(1)-1|<2, |z_(2)-2|<1 , then maximum value of |z_(1)+z_(2)| is.

If z_(1),z_(2),z_(3) satisfy the system of equations given by |z_(1)|=|z_(2)|=|z+3|=1,z_(1)+z_(2)+z_(3)=1 and z_(1)z_(2)z_(3)=1 such that lm(z_(1))

If z_(1)=iz_(2) and z_(1)-z_(3)=i(z_(3)-z_(2)), then prove that |z_(3)|=sqrt(2)|z_(1)|