Modulus & Argument: JEE Questions & Solutions

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

Let O be the origin, the point A be z₁ = √3 + 2√2i, the point B z₂ be such that √3|z₂| = |z₁| and arg(z₂) = arg(z₁) + π/6. Then:

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 - a)/(z + b) | = 1…

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

Let r and θ respectively be the modulus and amplitude of the complex number z = 2 - i(2 tan 5π/8). Then, (r, θ) is equal to:

If α denotes the number of solutions of |1 - i|^x = 2^x and β = |z|/arg(z), where z = π/4(1 + i)⁴ [(1 - √π i)/(√π + i) + (√π - i)/(1 + √π…

Let z = 1 + i and z₁ = (1 + iz)/(z(1-z) + 1/z). Then 12/π arg(z₁) is equal to.

The complex number z = (i-1)/(cos π/3 + i sin π/3) is equal to:

Let w₁ be the point obtained by the rotation of z₁ = 5 + 4i about the origin through a right angle in the anticlockwise direction, and w₂…

The number of real roots of the equation x|x|-5|x+2|+6=0 is

If the set { Re ((z- z+z z)/(2-3z+5 z)): z∈ℂ, Re(z)=3 } is equal to the interval (α,β], then 24(β-α) is equal to