Complex Numbers questions
967 published questions with worked solutions.
- The value of 1+ _ k=0 ^ 14 (2k+1) 15 +i (2k+1) 15 is
- 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
- 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
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