Practice questions
88551 published questions with worked solutions.
- Let z_1,z_2,z_3 be the affixes of the vertices of a triangle having the circumcentre at the origin. If z is the affix of it's...
- If | z-2 z+2 |= 6, then the locus of z is
- Locus of z, if ( z-1 z+1 )= 2, is
- If iz^3+z^2-z+i=0, then |z| is equal to
- The value of i (x-i)+i^2 +i^3 (x+i)+i^4 (2 ^ -1 x ), (where x>0 and i= -1 ), is
- The region of the complex plane for which | z-a z+ a |=1 [ Re (a) 0], is
- If 1 is any nth root of unity, then S=1+3 +5 ^2+ upon n terms, is equal to
- The maximum value of |z| where z satisfies the condition |z+ 2z |=2, is
- The value of i is
- 3+2i 1-2i will be real, if is
- For positive integers n_1,n_2 the value of the expression (1+i)^ n_1 + (1+i^3 )^ n_1 + (1+i^5 )^ n_2 + (1+i^7 )^ n_2 , i= -1 is a...
- 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