Question

Let z₁ & z₂ be complex numbers such that z₁ ≠ z₂ & |z₁| – |z₂|. If z₁ has positive real part and z₂ has negative imaginary part, then Z₁ + Z₂ / Z₁ - Z₂  may be 

(A) zero 

(B) real & positive 

(C) real & negative 

(D) purely imaginary

Answer 1

Correct option is (A, D)

Explanation:

 |Z₁| = |Z₂| ≠ a² + b² = c² + d²  Z₁ = a + iba > 0 Z₂ = c + idd < 0

(a + c) & (b + d) can be zero, so value can be zero (a – c) & 

(b – d) can be simultaneously zero ⇒ purely imaginary