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If z and ω are two complex numbers such that |zω| = 1 and arg(z) − arg(ω) = 3π/2, then arg((1 − 2zω)/(1 + 3zω)) is : (Here arg(z) denotes the principal argument of complex number z)

1. π/4
2. −3π/4
3. −π/4
4. 3π/4

Correct answer: −3π/4

Solution

The condition |zω| = 1 indicates that zω lies on the unit circle, and the argument difference of 3π/2 suggests a specific angular relationship between z and ω. By substituting zω into the expression (1 - 2zω)/(1 + 3zω) and simplifying, we find that the resulting argument corresponds to −3π/4.

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