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=(a2−b2)+2abi.

Equating real and imaginary parts we have,

a2−b2=0,2ab=1

The two real solutions to this pair of equations are

a=1√2,b=1√2 and a=−1√2,b=−1√2. The two square roots of i therefore are

±1√2(1+i)

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