Mathematics questions
18011 published questions with worked solutions.
- The centre of a square is at the origin and 1+i is one of its vertices. The extremities of its diagonals which does not pass...
- Which of the following statement is true? (i) The amplitude of the product of the two complex numbers is equal to product of...
- If ( 1) is a cube root of unity, then vmatrix 1&1+i+ ^2& ^2 1-i&-1& ^2-1 -i&-i+ -1&-1 vmatrix equals
- If z_1,z_2,z_3 be vertices of an equilateral triangle occurring in the anticlockwise sense, then
- If n is a positive integer greater than unity and z is a complex number satisfying the equation z^n=(z+1)^n, then
- The value of the determinant vmatrix 1+i&1-i&i 1-i&i&1+i &1+i&1-i vmatrix , where i= -1 is
- If Re ( z+4 2z-i )= 12, then z is represented by a point lying on
- If one vertex of a square whose diagonals intersect at the origin is 3( +i ), then the two adjacent vertices are
- The value of ( 1+i 3 1-i 3 )^6+ ( 1-i 3 1+i 3 )^6 is
- The greatest and the least value of |z_1+z_2|, if z_1=24+7i and |z_2|=6, are respectively
- If n Z, then 2^n (1-i)^ 2n + (1+i)^ 2n 2^n is equal to
- The polynomial x^ 3m +x^ 3n+1 +x^ 3k+2 is exactly divisible by x^2+x+1 if
- If +2 +3 = +2 +3 =0 and + + =n , then 3 +8 3 +27 3 =
- If x^2-2x +1=0, then x^ 2n -2x^n n +1 is equal to
- The curve represented by Im (z^2 )=k, where k is a non-zero real number, is
- For n=6k, k Z, ( 1-i 3 2 )^n+ ( -1-i 3 2 )^n has the value
- If z=re^ i , then |e^ iz | is equal to
- If _ 30^ ( 2|z|^2+2|z|-3 |z|+1 )<-2, then
- Let and be two fixed non-zero complex numbers and z' a variable complex number. If the lines z+ z+1=0 and z+ z-1=0 are mutually...
- The number of real solutions of the equation 6-x x^2-4 =2+ x x+2 , is