Practice questions
88551 published questions with worked solutions.
- ( -1+ 3i 2 )^ 100 + ( -1- 3i 2 )^ 100 is equal to
- If a= +i , b= +i , c= +i , and bc+ ca+ ab=1, then ( - )+ ( - )+ ( - ) is equal to
- The value of the expression 2 (1+ 1 ) (1+ 1 ^2 )+3 (2+ 1 ) (2+ 1 ^2 )+ +(n+1) (n+ 1 ) (n+ 1 ^2 ) is
- The value of (- 12+ 3i 2 )^ 1000 is
- One root of (1)^ 1/3 is
- A value of n such that ( 3 2+ i2 )^n=1 is
- Let a=e^ i 2 3 . Then the equation whose roots are a+a^ -2 and a^2+a^ -4 is
- The value of 1+ _ k=0 ^ 14 (2k+1) 15 +i (2k+1) 15 is
- If , and are angles such that + + = , and x= +i , y= +i and z= +i , then xyz is equal to
- If (x+iy)= 1+2i 3+4i , then (x^2+y^2)^2 is equal to
- If z^2+z+1=0, where z is a complex number, then the value of (z+ 1z )^2+ (z^2+ 1 z^2 )^2+ (z^3+ 1 z^3 )^2+ + (z^6+ 1 z^6 )^2 is
- If 3 2+ +i =a+ib, then [(a-2)^2+b^2 ] is equal to
- If x+iy = (a+ib), then -x-iy is equal to
- If ( 1) be a cube root of unity and (1+ ^2)^n=(1+ ^4)^n, then the least positive value of n is
- The minimum value of |a+b +c ^2|, where a,b,c are all not equal integers and ( 1) is a cube root of unity, is
- If is a complex cube root of unity, then the value of ^ 99 + ^ 100 + ^ 101 is
- If 1,a_1,a_2, ,a_ n-1 are the n roots of unity, then the value of (1-a_1)(1-a_2)(1-a_3) (1-a_ n-1 ) is equal to
- If is an imaginary cube root of unity, n is a positive integer but not a multiple of 3, then the value of 1+ ^n+ ^ 2n is
- Which of the following is a fourth root of 12+i 3 2?
- If n is a positive integer, then (1+i 3 )^n+ (1-i 3 )^n is equal to