Complex Numbers questions
967 published questions with worked solutions.
- If z=i (2- 3 ), then z=
- The general value of which satisfies the equation ( +i )( 3 +i 3 )( 5 +i 5 ) ( (2n-1) +i (2n-1) )=1 is
- If x_n= 3^n +i 3^n , then x_1 x_2 x_3 x_ is equal to
- 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 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
- 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 x^2-2x +1=0, then x^ 2n -2x^n n +1 is equal to
- 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
- 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...
- If , , be the roots of x^3+a^3=0 (a R), then the number of equation(s) whose roots are ( )^2 and ( )^2, is
- The common roots of the equations x^3+2x^2+2x+1=0 and 1+x^ 2002 +x^ 2003 =0 are (where is a complex cube root of unity)
- If z any complex number satisfying |z-3-2i| 2, then the minimum value of |2z-6+5i| is
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