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प्रश्न
The locus of z satisfying arg(z) = `pi/3` is ______.
उत्तर
The locus of z satisfying arg (z) = `pi/3` is `underlinebb(y = sqrt3x)`.
Explanation:
Let z = x + iy,
Then its polar form is z = r(cosθ + isinθ), Where tanθ = `y/x` and θ is arg(z).
Given that θ = `pi/3`.
Thus, `tan pi/3 = y/x` ⇒ y = `sqrt(3)x`, Where x > 0, y > 0.
Hence, locus of z is the part of y = `sqrt(3)x` in the first quadrant except origin.
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