If arg(z) < 0, then arg(-z) - arg(z) equals — JEE Main 2000 Mathematics PYQ

2000

\arg(z) < 0

, then

\arg(-z) - \arg(z)

equals

A.
$\pi$
B.
$-\pi$
C.
$-\pi/2$
D.
$\pi/2$

Show answer and solution

Correct option: A

Solution

If arg(z) < 0, let arg(z) = -θ where θ ∈ (0, π]. Then arg(-z) = arg(z) + π = -θ + π, which lies in (0, π], so it's a valid principal argument. Therefore arg(-z) - arg(z) = (-θ + π) - (-θ) = π.

[2000]

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