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