Home
Class 11
MATHS
Let z(1),z(2),z(3),...,z(n) be non zero ...

Let `z_(1),z_(2),z_(3),...,z_(n)` be non zero complex numbers with `|z_(1)|=|z_(2)|=|z_(3)|...=|z_(n)|` then the number `z=((z_(1)+z_(2))(z_(2)+z_(3))(z_(3)+z_(4))...(z_(n-1)+z_(n))(z_(n)+z_(1)))/(z_(1)z_(2)z_(3)...z_(n))` is

Promotional Banner

Similar Questions

Explore conceptually related problems

If |z_(1)|=|z_(2)|=|z_(3)|=......=|z_(n)|=1, then |z_(1)+z_(2)+z_(3)+......+z_(n)|=

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), z_(3) be three non-zero complex numbers such that z_(1) bar(z)_(2) = z_(2) bar(z)_(3) = z_(3) bar(z)_(1) , then z_(1), z_(2), z_(3)

Let z_(1),z_(2)..........z_(n) be equi-modular non-zero complex numbers such that z_(1)+z_(2)+z_(3)+...+z_(n)=0 Then Re(sum_(j=1)^(n)sum_(k=1)^(n)((z_(j))/(z_(k))))

Let z_(1) and z_(2) be two non-zero complex number such that |z_(1)|=|z_(2)|=|(1)/(z_(1)+(1)/(z_(2)))|=2 What is the value of |z_(1)+z_(2)| ?

If |z_(1)|=|z_(2)|=………….=|z-(n)|=1 , then the value of |z_(1)+z_(2)+………+z_(n)| , is

Let z_(1)z_(2),z_(3), be three complex number such that z_(1)+z_(2)+z_(3)=0 and |z_(1)|=|z_(2)|=|z_(3)|=1 then Let |z_(1)^(2)+2z_(2)^(2)+z_(3)^(2)| equals

if z_(1),z_(2),z_(3),…..z_(n) are complex numbers such that |z_(1)|=|z_(2)| =….=|z_(n)| = |1/z_(1) +1/z_(2) + 1/z_(3) +….+1/z_(n)| =1 Then show that |z_(1) +z_(2) +z_(3) +……+z_(n)|=1

If |z_(1)|=|z_(2)|=......=|z_(n)|=1, prove that |z_(1)+z_(2)+z_(3)++z_(n)|=(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))++(1)/(z_(n))