Write the value of the square root of i.

1.	Write the value of the square root of i.
Answer» Let \(\sqrt{i}\) = \(\sqrt{a+ib}\) .........….1 Squaring both sides, we get i² = (a²- b²) +2aib By comparing real and imaginary term, we get 2ab = 1 and a²- b²= 0 By solving these we get a = b = \(\frac{1}{\sqrt{2}}\) By putting value of a and b in 1, we get \(\sqrt{i}\) = ± \(\frac{1}{\sqrt{2}}\) + \(\frac{1}{\sqrt{2}}\)i \(\sqrt{i}\) = ± \(\frac{1}{\sqrt{2}}\) (1+i)

Answer»

Let

\(\sqrt{i}\) = \(\sqrt{a+ib}\) .........….1

Squaring both sides, we get

i² = (a²- b²) +2aib

By comparing real and imaginary term, we get

2ab = 1 and a²- b²= 0

By solving these we get

a = b = \(\frac{1}{\sqrt{2}}\)

By putting value of a and b in 1, we get

\(\sqrt{i}\) = ± \(\frac{1}{\sqrt{2}}\) + \(\frac{1}{\sqrt{2}}\)i

\(\sqrt{i}\) = ± \(\frac{1}{\sqrt{2}}\) (1+i)

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