If `|z_(1)-z_(0)|=|z_(2)-z_(0)|=a and "amp" ((z_(2)-z_(0))/(z_(0)-z_(1)))=(pi)/(2)` then find `z_(0)`.

If (z)_(1)=2-i , (z)_(2)=1+i , find |((z)_(1)+(z)_(2)+1)/((z)_(1)-(z)_(2)+1)|

If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1) + z_(2)| = |z_(1)| + |z_(2)| , then arg ((z_(1))/(z_(2))) is equal to a)0 b) -pi c) -(pi)/(2) d) (pi)/(2)

If z_(1), z_(2),……..,z_(n) are complex numbers such that |z_(1)| = |z_(2)| = …….. = |z_(n)| = 1 , then |z_(1) + z_(2) +……..+ z_(n)| is equal to a) |z_(1)z_(2)z_(3)…..z_(n)| b) |z_(1)|+|z_(2)|+…….+|z_(n)| c) |(1)/(z_(1)) + (1)/(z_(2)) + ……….+ (1)/(z_(n))| d)n

For two unimodular complex numbers Z_(1) and Z_(2), [(bar(z_(1)),-z_(2)),(bar(z_(2)),z_(1))]^(-1)[(z_(1),z_(2)),(-bar(z_(2)),bar(z_(1)))]^(-1) is equal to a) [(z_(1),z_(2)),(bar(z)_(1),bar(z)_(2))] b) [(1,0),(0,1)] c) [(1//2,0),(0,1//2)] d)None of these

If |z_(1) + z_(2)|=|z_(1)-z_(2)| , then the difference in the amplitudes of z_(1) and z_(2) is

If |z_(1)|= |z_(2)|= |z_(3)|=1 and z_(1) , z_(2), z_(3) are represented by the vertices of an equilateral triangle then which of the following is true?