Complex Numbers questions
967 published questions with worked solutions.
- If = -1+ 3i 2, then (3+ +3 ^2)^4 is
- If n is an integer which leaves remainder one when divided by three, then (1+ 3i )^n+ (1- 3i )^n equals
- The smallest positive integral value of n such that [ 1+ 8+i 8 1+ 8-i 8 ]^n is purely imaginary, is equal to
- The value of ( 2+i 2 ) ( 4+i 4 ) ( 8+i 8 ) is
- The value of a+b +c ^2 b+c +a ^2 + a+b +c ^2 c+a +b ^2 will be
- If is a complex cube root of unity, then the value of ( ^ 10 + ^ 23 ) - 6 is
- If x+iy= a+ib c+id , then x^2+y^2 is equal to
- The value of the expression 1 (2- )(2- ^2)+2 (3- )(3- ^2)+ +(n-1)(n- )(n- ^2), where is an imaginary cube root of unity is
- If iz^4+1=0, then z can be take the value
- If is a complex cube root of unity, then a+b +c ^2 c+a +b ^2 + c+a +b ^2 a+b +c ^2 + b+c +a ^2 b+c ^4+a ^5 is equal to
- The value of _ k=1 ^ 10 ( 2k 11 +i 2k 11 ) is
- Let x= + , y= + ^2, z= ^2+ , is an imaginary cube root of unity. The value of xyz is
- 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...
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