\(\rm \sqrt{3}\) - i के आयाम का प्रमुख मान क्या है?

  1. -π/3
  2. π/6
  3. π/3
  4. -π/6

Answer (Detailed Solution Below)

Option 4 : -π/6
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अवधारणा:

जब z = x + iy तब एक सम्मिश्र संख्या का प्रमुख आयाम θ = tan-1(\(\rm \frac{y}{x}\))

tan \(\rm \frac{\pi }{6}\) = \(\rm \frac{1}{{\sqrt{3}}}\)

x > 0, y < 0, IVवें चतुर्थांश में बिंदु निहित है।

गणना:

मान लीजिए θ, \(\rm \sqrt{3}\) - i के आयाम का प्रमुख मान है

के बाद से, tan θ = \(\rm \frac{-1}{{\sqrt{3}}}\) और \(\rm \sqrt{3}\) - i IVवें चतुर्थांश में बिंदु निहित है।

tan θ = tan (-\(\rm \frac{\pi }{6}\)), θ = -\(\rm \frac{\pi }{6}\)

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