Which one of the following is a square root of , where a, b ∈ ℝ?

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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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Formula used:

(a + b)2 = a2 + b2 + 2ab

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

i2 = -1

Concept Used:

if y = x2 then we can say that x is the square root of y

Calculation:

We have the algebric expression 

⇒ {(a + ib) + (a - ib)} + 

⇒ 

⇒ 

∴ The square root of   is  .

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