If `z^4+1=sqrt(3)i` (A) `z^3` is purely real (B) z represents the vertices of a square of side `2^(1/4)` (C) `z^9` is purely imaginary (D) z represents the vertices of a square of side `2^(3/4)`

If (z+1)/(z+i) is a purely imaginary number (where (i=sqrt(-1) ), then z lies on a

If z_(1)=1+2i, z_(2)=2+3i, z_(3)=3+4i , then z_(1),z_(2) and z_(3) represent the vertices of a/an.

The vertices of a square are z_1,z_2,z_3 and z_4 taken in the anticlockwise order, then z_3=

if (5z_2)/(7z_1) is purely imaginary number then |(2z_1+3z_2)/(2z_1-3z_2) | is equal to

If a ,b ,c are nonzero real numbers and a z^2+b z+c+i=0 has purely imaginary roots, then prove that a=b^2c

If z is a unimodular number (!=+-i) then (z+i)/(z-i) is (A) purely real (B) purely imaginary (C) an imaginary number which is not purely imaginary (D) both purely real and purely imaginary

bb"statement-1" " Let " z_(1),z_(2) " and " z_(3) be htree complex numbers, such that abs(3z_(1)+1)=abs(3z_(2)+1)=abs(3z_(3)+1) " and " 1+z_(1)+z_(2)+z_(3)=0, " then " z_(1),z_(2),z_(3) will represent vertices of an equilateral triangle on the complex plane. bb"statement-2" z_(1),z_(2),z_(3) represent vertices of an triangle, if z_(1)^(2)+z_(2)^(2)+z_(3)^(2)+z_(1)z_(2)+z_(2)z_(3)+z_(3)z_(1)=0

If |z_1|=|z_2| and arg((z_1)/(z_2))=pi , then z_1+z_2 is equal to (a) 0 (b) purely imaginary (c) purely real (d) none of these

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot

If 2z_1//3z_2 is a purely imaginary number, then find the value of "|"(z_1-z_2")"//(z_1+z_2)|dot