Practice questions
88551 published questions with worked solutions.
- If , , are the cube roots of a negative number p, then for any three real numbers x,y,z the value of x +y +z x +y +z is
- One of the values of ( 1+i 2 )^ 2/3 is
- The square roots of -7,-24 -1 are
- If 2x=-1+ 3i, then the value of (1-x^2+x )^6- (1-x+x^2 )^6 is equal to
- If is a complex cube root of unity, then ( ^ 10 + ^ 23 ) - 4 is equal to
- The value of (2- )(2- ^2)(2- ^ 10 )(2- ^ 11 ), where is the complex cube root of unity, is
- If ( 1+ +i 1+ -i )^n=u+iv, where u and v all real numbers, then u is
- If ( +i )( 2 +i 2 ) ( n +i n )=1, then the value of is
- 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