JEE Main 2021 — Complex Number Questions with Solutions

Let z 1 , z 2 be the roots of the equation z 2 + a z + 12 = 0 and z 1 ,   z 2 form an equilateral triangle with or…

Let a complex number be w = 1 - 3 i . Let another complex number z be such that | z w | = 1 and arg z - arg w = π…

Let z be those complex numbers which satisfy z + 5 ≤ 4 and z 1 + i + z ¯ 1 - i ⩾ - 10 , i = - 1 . If…

The equation of a circle is Re z 2 + 2 Im z 2 + 2 Re z = 0 , where z = x + i y . A line which passes through the centre…

Let n denote the number of solutions of the equation z 2 + 3 z ¯ = 0 , where z is a complex number. Then the value…

If for the complex numbers   z satisfying | z - 2 - 2 i | ≤ 1 , the maximum value of | 3 i z + 6 | is attain…

If ( 3 + i ) 100 = 2 99 ( p + i q ) , then p and q are roots of the equation :

If the real part of the complex number z = 3 + 2 i cos θ 1 - 3 i cos θ , θ ∈ 0 , π 2 is zero,…

A point z moves in the complex plane such that arg z - 2 z + 2 = π 4 , then the minimum value of | z - 9 2 - 2 i |…

Let S 1 ,   S 2 and S 3 be three sets defined as S 1 = { z ∈ ℂ : | z - 1 | ≤ 2 } , S 2 = { z &#8…