" 64."|z-(z_(1)+z_(2))/(2)|^(2)+|(z_(1)-z_(2))/(2)|^(2)=

Z-(Z_(1)+Z_(1))/(2)|^(2)+|(Z_(1)-Z_(2))/(2)|^(2)=

For three non-colliner complex numbers Z,Z_(1) and Z_(2) prove that |Z-(Z_(1)+Z_(2))/(2)|^(2) + |(Z_(1) -Z_(2))/(2)|^(2)= (1)/(2) | Z - Z_(1)|^(2) +(1)/(2)|Z- 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)|=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

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))

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 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)

For any two complex numbers z_(1) and z_(2) |z_(1)+z_(2)|^(2) =(|z_(1)|^(2)+|z_(2)|^(2))