JEE Main 2024 — Complex Number Questions with Solutions

Let P = z ∈ ℂ : z + 2 − 3 i ≤ 1 and Q = z ∈ ℂ : z 1 + i + z ¯ 1 − i ≤ − 8 . Let in P ∩ Q , z − 3 + 2 i be maximum and m…

Let α , β be the roots of the equation x 2 - x + 2 = 0 with Im ( α ) > Im ( β ) . Then α 6 + α 4 + β 4 - 5 α 2 is equal…

Let z be a complex number such that the real part of (z-2 i)/(z+2 i) is zero. Then, the maximum value of |z-(6+8 i)| is…

Let z be a complex number such that |z+2|=1 and Im ((z+1)/(z+2) )=(1)/(5). Then the value of |Re(z+2)| is

Let α , β be the roots of the equation x 2 - 6 x + 3 = 0 such that Im ( α ) > Im ( β ) . Let a , b be integers not divi…

The sum of all possible values of θ [-π, 2 π], for which (1+i θ)/(1-2 i θ) is purely imaginary, is equal

Let the complex numbers α and 1 α ¯ lie on the circles z - z 0 2 = 4 and z - z 0 2 = 16 respectively, where z 0 = 1 + i…

If S = z ∈ C : | z - i | = | z + i | = | z - 1 | , then, n ( S ) is:

If z is a complex number such that z ≤ 1 , then the minimum value of z + 1 2 3 + 4 i is:

The sum of the square of the modulus of the elements in the set \z=a+ib: a, b Z, z C,|z-1| ≤ 1,|z-5| ≤|z-5 i|\ is _____…