The `omega!=` 1 is nth root unity, then value of `sum_(k=0)^(n-1)|z_1+omega^k z_2|^2` is `n(|z_1|^2+|z_2|^2)` b. `|z_1|^2+|z_2|^2` c. `(|z_1|+|z_2|)^2` d. `n(|z_1|+|z_2|)^2`

if omega is the nth root of unity and Z_1 , Z_2 are any two complex numbers , then prove that . Sigma_(k=0)^(n-1)| z_1+ omega^k z_2|^2=n{|z_1|^2+|z_2|^2} where n in N

If z_1, z_2 in C , then say which are true and false - . |z_1+z_2|^2=|z_1""|^2+|z_2|^2-2R e(z_1 z_2) |z_1-z_2|^2=|z_1""|^2-|z_2|^2-2R e(z_1 z_2) |z_1+z_2|^2+|z_1-z_2|^2=2(|z_1|^2+|z_2|^2) |a z_1-b z_2|^2+|b z_1+a z_2|^2=(a^2+b^2)(|z_1|^2+|z_2|^2) , where a ,b in Rdot

For any two complex numbers z_1 and z_2 prove that: |\z_1+z_2|^2=|\z_1|^2+|\z_2|^2+2Re bar z_1 z_2

If |z_1|=1a n d|z_2|=2,t h e n Max (|2z_1-1+z_2|)=4 Min (|z_1-z_2|)=1 |z_2+1/(z_1)|lt=3 Min (|z_1=z_2|)=2

For any two 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|=|z_2|=1, then prove that |z_1+z_2| = |1/z_1+1/z_2∣

Find the greatest and the least value of |z_1+z_2| if z_1=24+7ia n d|z_2|=6.

Find the greatest and the least value of |z_1+z_2| if z_1=24+7ia n d|z_2|=6.

If |z_1|=|z_2|=|z_3|=1 then value of |z_1-z_3|^2+|z_3-z_1|^2+|z_1-z_2|^2 cannot exceed

z_1a n dz_2 lie on a circle with center at the origin. The point of intersection z_3 of he tangents at z_1a n dz_2 is given by 1/2(z_1+( z )_2) b. (2z_1z_2)/(z_1+z_2) c. 1/2(1/(z_1)+1/(z_2)) d. (z_1+z_2)/(( z )_1( z )_2)