JEE Main Mathematics — Complex Number Previous-Year Questions

Let z be the complex number satisfying |z-5| ≤ 3 and having maximum positive principal argument. Then 34 |5 z-125 i z+1…

Let α=-1+i √(3)2 and β=-1-i √(3)2, i=√(-1). If (7-7 α+9 β)²⁰+(9+7 α-7 β)²⁰+(-7+9 α+7 β)²⁰+(14+7 α+7 β)²⁰=m¹⁰, then m is…

The number of values of z C, satisfying the equations |z-(4+8i)|=√(10) and |z-(3+5i)|+|z-(5+11i)|=4√(5), is:

Let the circles C₁ : |z| = r and C₂ : |z - 3 - 4i| = 5, z C, be such that C₂ lies within C₁. If z₁ moves on C₁, z₂ move…

Let z₁, z₂ C be the distinct solutions of the equation z² + 4z - (1 + 12i) = 0. Then |z₁|² + |z₂|² is equal to :

Let S= \z C: 4 z²+z=0 \. Then S|z|² is equal to:

Let A=\z C:|z-2| 4\ and B=\z C:|z-2|+|z+2|=5\. Then the max |z₁-z₂ |: z₁ ~A . and .z₂ ~B \ is :

Let the set of all values of k R such that the equation z(z + 2 + i) + k(2 + 3i) = 0, z C, has at least one solution, b…

Let x and y be real numbers such that 50 ((2x)/(1+3i) - (y)/(1-2i) ) = 31 + 17i, i = √(-1). Then the value of 10(x - 3y…

Let S=\z: 3 |2 z-3(1+i)| 7\ be a set of complex numbers. Then z S | (z+(1)/(2)(5+3 i) ) | is equal to :