[" If "2 pi" 6."],[qquad |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2|z_(1)|^(2)+2|z_(2)|^(2)]

Prove that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)=2|z_(1)|^(2) + 2|z_(2)|^(2)

If z_(1)=3 + 4i,z_(2)= 8-15i , verify that |z_(1) + z_(2)|^(2) + |z_(1)-z_(2)|^(2)= 2(|z_(1)|^(2) + |z_(2)|^(2))

For all complex numbers z_(1) and z_(2) , prove that |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2(|z_(1)|^(2)+|z_(2)|^(2)) .

If z_(-)1 and z_(-)2 are any two complex numbers show that |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2|z_(1)|^(2)+2|z_(2)|^(2)

If z_(1) and z_(2) are two complex quantities, show that, |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2[|z_(1)|^(2)+|z_(2)|^(2)].

If z;z_(1);z_(2)varepsilon C then (vii) |z_(1)+z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)+2Re(z_(1)bar(z)_(2))( viii) |z_(1)-z_(2)|^(2)=|z_(1)|^(2)+|z_(2)|^(2)-2Re(z_(1)bar(z)_(2))( ix) |z_(1)+z_(2)|^(2)+|z_(1)-z_(2)|^(2)=2(|z_(1)|^(2)+|z_(2)|^(2))(x)|az_(1)-bz_(2)|^(2)+|bz_(1)+az_(2)|^(2)=(a^(2)+b^(2))(|z_(1)|^(2)+|z_(2)|^(2)) where a;b varepsilon R

For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) =(|z_(1)|^(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)|=1,|z_(2)|=2,|z_(3)|=3 ,then |z_(1)+z_(2)+z_(3)|^(2)+|-z_(1)+z_(2)+z_(3)|^(2)+|z_(1)-z_(2)+z_(3)|^(2)+|z_(1)+z_(2)-z_(3)|^(2) is equal to