Mathematics questions
18011 published questions with worked solutions.
- Let z be a complex number satisfying |z-5i| 1 such that amp (z) is minimum. Then z is equal to
- The value of sum _ n=1 ^ 13 (i^n+i^ n+1 ), where i= -1 , equals
- If z is a complex number, then the minimum value of |z|+|z-1| is
- If is a complex root of the equation z^3=1, then + ^ ( 12+ 38+ 9 32 + 27 128 + ) is equal to
- If is a complex cube root of unity, then value of vmatrix x+1& & ^2 &x+ ^2&1 ^2&1&x+ vmatrix is
- If the area of the triangle on the complex plane formed by the points z, z+iz, and iz is 200, then the value of |3z| must be...
- Statement 1: If | zz_1-z_2 zz_1+z_2 |=k, (z_1,z_2 0), then the locus of z is circle Statement 2: As | z-z_1 z-z_2 |= represents a...
- Re (z^2 )=1 is represented by
- If z z=0, iff
- The locus of the point z which satisfy the condition ( z-1 z+1 )= 3, is
- If |z_1|=|z_2|= =|z_n|=1, then the value of |z_1+z_2+z_3+ +z_n| is
- If complex numbers z_1,z_2 and z_3 represent the vertices A,B and C respectively of an isosceles triangle ABC of which C is right...
- -1- -1- -1- is equal to
- The imaginary part of (z-1)( -i )+(z-1)^ -1 ( +i ) zero, if
- ( z) is equal to
- The point of intersection of the curves (z-3i)= 3 4 and (2z+1-2i)= 4 (where i= -1 ) is
- Given z= q+ir 1+p , then p+iq 1+r = 1+iz 1-iz if
- If is a complex cube root of unity, then for positive integral value of n, the product of ^2 ^3 ^n will be
- Statement 1: If (1-i)=a+ib, where a,b R and i= -1 , then a= 12 (e+ 1e ) 1, b= 12 (e- 1e ) 1 Statement 2: e^ i = +i
- If |a_k|<1, _k 0 for k=1,2, ,n and _1+ _2+ + _n=1, then the value of | _1a_1+ _2a_2+ + _na_n| is