If `a m p(z_1z_2)=0a n d|z_1|=|z_2|=1,t h e n` `z_1+z_2=0` b. `z_1z_2=1` c. `z_1=z _2` d. none of these

If |z_1| = |z_2| =1 and amp z_1 +amp z_2 =0 then

If z_1ne-z_2 and |z_1+z_2|=|1/z_1 + 1/z_2| then :

The complex numbers z_1, z_2 and the origin form an equilateral triangle only if (A) z_1^2+z_2^2-z_1z_2=0 (B) z_1+z_2=z_1z_2 (C) z_1^2-z_2^2=z_1z_2 (D) none of these

If |z_1|=1,|z_2|=1 then prove that |z_1+z_2|^2+|z_1-z_2|^2 =4.

If |z_1+z_2|=|z_1-z_2| and |z_1|=|z_2|, then (A) z_1=+-iz_2 (B) z_1=z_2 (C) z_=-z_2 (D) z_2=+-iz_1

If z_1,z_2,z_3,………..z_(n-1) are the roots of the equation 1+z+z^2+…….+z^(n-1)=0, where n epsilon N, ngt2 then (A) z_1,z_2, …z_(n-1) are terms of a G.P. (B) z_1,z_2,……,z_(n-1) are terms of an A.P. (C) |z_1|=|z_2|=|z_3|=.|z_(n-1)|!=1 (D) none of these

Statement I: If |z_1+z_2|=|z_1|+|z_2|, then Im(z_1/z_2)=0 (z_1,z_2 !=0) Statement II: If |z_1+z_2|=|z_1|+|z_2| then origin, z_1, z_2 are collinear with 'z_1' and z_2 lies on the same side of the origin (z_1,z_2 !=0)

Suppose z_1 + z_2 + z_3 + z_4=0 and |z_1| = |z_2| = |z_3| = |z_4|=1. If z_1, z_2, z_3 ,z_4 are the vertices of a quadrilateral, then the quadrilateral can be a (a) parallelogram (c) rectangle (b) rhombus (d) square

For two unimodular complex number z_1a n dz_2 [( z )_1-z_2( z )_2z_1]^(-1)[( z )_1z_2-( z )_2z_1]^(-1) is equal to [z_1z_2( z )_1( z )_2]^ b. [1 0 0 1] c. [1//2 0 0 1//2] d. none of these