Practice questions
88551 published questions with worked solutions.
- If 1, , ^2 are the cube roots of unity, then ^2(1+ )^3-(1+ ^2) is equal to
- If is a cube root of unity, then the value of (1- + ^2 )^5+ (1+ - ^2 )^5 is
- The value of _ k=1 ^6 [ ( 2k 7 )-i ( 2k 7 ) ] is
- If 1, , ^2 are the cube roots of unity, then (3+ ^2+ ^4 )^6 is equal to
- If 1, , ^2 are the cube roots of unity, then (1- + ^2 ) (1- ^2+ ^4 ) (1- ^4+ ^8 ) (1- ^8+ ^ 16 ) upto 2n factors is
- If w= z z- 13i and |w|=1, then z lies on
- The locus of point z satisfying Re ( 1z )=k, where k is a non-zero real number, is
- The centre of a regular hexagon is at the point z=i. If one of its vertices is at 2+i, then the adjacent vertices of 2+i are at...
- For all complex numbers z_1,z_2 satisfying |z_1|=12 and |z_2-3-4i|=5, the minimum value of |z_1-z_2| is
- Let z=x+iy be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the roots of the...
- Let z_1 and z_2 be the roots of the equation z^2+pz+q=0 where p,q are real. The points represented by z_1,z_2 and the origin form...
- The equation z z+a z+ az+b=0, b R represents a circle, if
- If magnitude of a complex number 4-3i is tripled and is rotated anti-clockwise by an angle , then resulting complex number would...
- If | z+i z-i |= 3, then radius of the circle is
- If the area of triangle on the argand plane formed by the complex numbers -z, iz, z-iz is 600 sq. unit, then |z| is equal to
- The locus represented by the equation |z-1|=|z-i| is
- If z_1,z_2 and z_3 are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are z_1,z_2...
- The equation of the locus of z such that | z-i z+i |=2, where z=x+iy is a complex number, is
- The set C= z:z z+a z+ az+b=0, b R and b<|a|^2 is
- The locus of the points z which satisfy the condition ( z-1 z+1 )= 3 is