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1987

JEE Main 1987 Mathematics question on Complex Numbers and Quadratic Equations

If z1z_1 and z2z_2 are two non-zero complex numbers such that ∣z1+z2∣=∣z1∣+∣z2∣|z_1 + z_2| = |z_1| + |z_2|, then arg⁡(z1)−arg⁡(z2)\arg(z_1) - \arg(z_2) is equal to
  1. A.
    −π-\pi
  2. B.
    −π2-\dfrac{\pi}{2}
  3. C.
    00
  4. D.
    π2\dfrac{\pi}{2}
Show answer and solution

Correct option: C

Solution

|z₁ + z₂| = |z₁| + |z₂| holds if and only if z₁ and z₂ point in the same direction in the complex plane, i.e., they are non-negative real multiples of each other. This means arg(z₁) = arg(z₂), so arg(z₁) - arg(z₂) = 0.

[1987]

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