# Let, (a + ib)2 = 1 + 4 i

Now using, (a + b)2 = a2 + b2 + 2ab a2 + (bi)2 + 2abi = 1 + 4 i

Since i2 = -1 a2 - b2 + 2abi = 1 + 4 i

Now, separating real and complex parts, we get a2 - b2 = 1…………..eq.1 2ab =4 …….eq.2 a = Now, using the value of a in eq.1, we get – b2 = 1 12 – b4 = b2 b4 + b2 - 12= 0

Simplify and get the value of b2 , we get, b2 = -4 or b2 = 3

as b is real no. so, b2 = 3

b= or b= Therefore, a= 2 or a= -2

Hence the square root of the complex no. is 2 + i and -2 - i.

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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics