निम्नलिखित में से कौन  का वर्गमूल है, जहां a, b ∈ ℝ दिया गया है?

जहां i = √-1

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NDA 02/2021: Maths Previous Year paper (Held On 14 Nov 2021)
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  1. 2a + ib
  2. 2a - ib

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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प्रयुक्त सूत्र:

(a + b)2 = a2 + b2 + 2ab

(a + ib) (a - ib) = a2 - i2b2 = a2 + b2

i2 = -1

प्रयुक्त अवधारणा:

यदि y = x2 है तो हम कह सकते हैं कि x, y का वर्गमूल है

गणना:

हमारे पास बीजीय व्यंजक  है

⇒ {(a + ib) + (a - ib)} + 

⇒ 

⇒ 

∴   का वर्गमूल  है। 

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