If i=√−1, is √i imaginary?
Is it used or considered often in mathematics? How is it notated?
Let z=(a+bi) be a complex number which is a square root of i, that is
Equating real and imaginary parts we have,
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