COMPLEX NUMBERS | nth Root of Unity |JEE | 11 Maths | 4 PM By Pallavi Ma'am | L20 | English Medium

JEE Mains & Advanced | Chemistry - Ideal Gases By Vipin Sir | L4 English Medium

Let alpha be the non-real 5 th root of unity. If z_1 and z_2 are two complex numbers lying on |z| = 2 , then the value of sum_(t=0) ^(4) |z_1 + alpha ^(t)z_2 |^(2) is ______ .

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

Match the following : {:("Column-I" ," Column-II"),("(A) The value of " underset(k=1)overset(2007)sum (sin""(2kpi)/9 - icos""(2kpi)/9) " is" , " (p) -1"),("(B) If " z_(1)","z_(2) and z_(3) " are unimodular complex numbers such that " |z_(1)+z_(2)+z_(3)|=1 " then " |1/z_(1)+1/z_(2) + 1/z_(3)| " is equal to " , " (q) 2 "),("(C) If the complex numbers " z_(1)"," z_(2) and z_(3) " represent the vetices of an equilateral triangle such that " |z_(1)|=|z_(2)|=|z_(3)| " then " (z_(1) +z_(2) +z_(3)) -1 " is equal to " , " (r) 1"),("(D) If " alpha " is an imaginary fifth root of unity , then " 4log_(4)| 1+alpha +alpha^(2) +alpha^(3) -1/alpha| " is " , " (s) 0"):}

Triangle - Inequality | cube root and nth roots of Unity | Roots of any Complex-Number Questions

12:30 PM JEE Mains 2020 - Maths | Complex Numbers - 30 Days Score Booster Course