Question 5:- The region represented by {z = x + iy ∈ C : |z| – Re(z) ≤ 1} is also given by the inequality : (A) y² ≤ x + 1/2 (B) y² ≤ 2(x + 1/2) (C) y² ≥ x + 1 (D) y² ≥ 2(x + 1) Solution:- Given that, z = … Read more
Question 4:- If Re(z-1/2z+i) = 1, where z = x + iy, then the point (x, y) lies on a : (A) Straight line whose slope is -2/3 (B) Straight line whose slope 3/2 (C) Circle whose diameter is √5/2 (D) Circle whose centre is at (-1/2, -3/2) Solution:- Since, z = x + iy … Read more
Question 3:- If w = α + iβ where β ≠ 0 and z ≠ 1 satisfies that condition that is purely real, then the set of values of z is (a) |z| = 1, z ≠ 2 (b) |z| = 1 and z ≠ 1 (c) … Read more
Question 2:- Let complex numbers α and lies on circles and , respectively. If satisfies the equation , then |α| is equal to (2013 Adv.) Solution:- Intersection of circles, the basic concept is to equations simultaneously and using properties of modulus of complex numbers. We know that, and Here, and could be written as and … Read more