JEE Main 2025 — Complex Number Questions with Solutions

Let integers a, b [-3,3] be such that a+b ≠ 0. Then the number of all possible ordered pairs (a, b), for which |z-az+b…

Let the curve z(1+i)+z(1-i)=4, z C, divide the region |z-3| ≤ 1 into two parts of areas α and β. Then |α-β| equals :

If the locus of z C, such that Re (z-12 z+i )+Re (z-12 z-i )=2 is a circle of radius r and center (a, b) then (15 a b)/…

Let O be the origin, the point A be z₁=√(3)+2 √(2) i, the point B (z₂ ) be such that √(3) |z₂ |= |z₁ | and (z₂ )= (z₁ )…

Among the statements (S1) : The set \z C-\-i |z|=1 . and z-iz+i is purely real} contains exactly two elements, and (S2)…

Let z be a complex number such that |z|=1. If 2+k² zk+z=kz, k R, then the maximum distance of k+ik² from the circle |z-…

Let α, β be the roots of the equation x²-a x-b=0 with Im(α) Im(β). Let Pn=αⁿ-βⁿ. If P₃=-5 √(7) i, P₄=-3 √(7) i, P₅=11 √…

Let |z₁-8-2 i | ≤ 1 and |z₂-2+6 i | ≤ 2, z₁, z₂ C . Then the minimum value of |z₁-z₂ | is :

Let |z-i2 z+i |=(1)/(3), z C, be the equation of a circle with center at C. If the area of the triangle, whose vertices…

The number of complex numbers z, satisfying |z|=1 and |zz+zz |=1, is :