Practice questions
88551 published questions with worked solutions.
- The equation z z+(4-3i)z+(4+3i) z+5=0 represents a circle of radius
- The complex numbers z_1,z_2,z_3,z_4 taken in that order in the Argand plane represent the vertices of a parallelogram iff
- If z 0 be a complex number and (z)= /4, then
- Given that a' is a fixed complex number, and ' is a scalar variable, the point z satisfying z=a(1+i ) traces out
- The value of expression (1+ 1 ) (1+ 1 ^2 )+ (2+ 1 ) (2+ 1 ^2 )+ (3+ 1 ) (3+ 1 ^2 )+ + (n+ 1 ) (n+ 1 ^2 ), where is an imaginary...
- If A+ B+ C=0, A+ B+ C=0 and A+B+C=180^ , then the value of 3A+ 3B+ 3C is
- If 1, , ^2 are the cube roots of unity, then vmatrix 1+ & ^2&- 1+ ^2& &- ^2 ^2+ & &- ^2 vmatrix =
- If a+b+c 0, then (a+b +c ^2)^3+(a+b ^2+c )^3=
- If a= 2i , then which of the following is correct?
- The locus of the point z satisfying ( z-1 z+1 )=k, where k is non-zero real, is
- If |z_1|=|z_2|=|z_3| and z_1+z_2+z_3=0, then z_1,z_2,z_3 are vertices of
- If a,b,c and u,v, are complex numbers representing the vertices of two triangles such that c=(1-r)a+rb and =(1-r)u+rv, where r is...
- Let z_1,z_2,z_3 be three vertices of an equilateral triangle circumscribing the circle |z|= 12. If z_1= 12+i 3 2 and z_1,z_2,z_3...
- If p^2-p+1=0, then the value of p^ 3n can be
- If is a complex cube root of unity, then (1+i)^ 2n -(1-i)^ 2n (1+ ^4- ^2 ) (1- ^4+ ^2 ) is equal to
- Let z_1 and z_2 be two complex numbers such that z_1 z_2 + z_2 z_1 =1. Then,
- If z_1 and z_2 are two complex numbers such that | z_1-z_2 1- z_1z_2 |=1, then which one of the following is not true?
- The area of the triangle whose vertices are i, and ^2, where i= -1 and , ^2 are complex cube roots of unity, is
- If ( 3/2+(1/2)i 3/2-(1/2)i )^ 120 =p+iq, then
- If 2z_1-3z_2+z_3=0, then z_1,z_2,z_3 are represented by