What is √i\sqrt{i}?

If i=1, is i imaginary?

Is it used or considered often in mathematics? How is it notated?

Answer

Let z=(a+bi) be a complex number which is a square root of i, that is
i=z2=(a2b2)+2abi.
Equating real and imaginary parts we have,
a2b2=0,2ab=1

The two real solutions to this pair of equations are
a=12,b=12 and a=12,b=12. The two square roots of i therefore are

±12(1+i)

Attribution
Source : Link , Question Author : Gordon Gustafson , Answer Author : Jyotirmoy Bhattacharya

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