JEE Main 2023 — Complex Number Questions with Solutions

Let z = 1 + i and z 1 = 1 + i z ¯ z ¯ ( 1 - z ) + 1 z · Then 12 π arg z 1 is equal to

Let A = θ ∈ 0 ,   2 π : 1 + 2 i sin θ 1 - i sin θ   is   purely   imagina…

If for z = α + i β ,   z + 2 = z + 4 ( 1 + i ) , then α + β and α β are the roots of…

For α ,   β ,   z ∈ ℂ and λ > 1 , if λ - 1 is the radius of the circle z…

Let z 1 = 2 + 3 i and z 2 = 3 + 4 i . The set S = z ∈ C : z - z 1 2 - z - z 2 2 = z 1 - z 2 2 represents a

Let S = z ∈ ℂ : z ¯ = i z 2 + Re ( z ¯ ) . Then ∑ z ∈ S | z | 2 is equal to

If the center and radius of the circle z - 2 z - 3 = 2 are respectively α , β and γ , then 3 α + &#…

Let S = z = x + i y : 2 z - 3 i 4 z + 2 i is a real number } . Then which of the following is NOT correct?

Let the complex number z = x + i y be such that 2 z - 3 i 2 z + i is purely imaginary. If x + y 2 = 0 , then y 4 + y 2…

Let S = z ∈ ℂ - { i , 2 i } : z 2 + 8 i z - 15 z 2 - 3 i z - 2 ∈ ℝ . α - 13 11 i ∈ S…