Answer:
(1/√2) + (1/√2)i
Explanation:
The value of the square root of the imaginary unit, √i, can be calculated as follows:
Let's express i in exponential form: i = e^(iπ/2) (Euler's formula).
Taking the square root of both sides, we get: √i = √(e^(iπ/2)).
Using the properties of exponents and the square root, we have: √(e^(iπ/2)) = e^(iπ/4).
Therefore, the value of the square root of the imaginary unit, √i, is e^(iπ/4).
In polar form, this can be represented as √i = cos(π/4) + i*sin(π/4).
Simplifying further, we get √i = (1/√2) + i*(1/√2).
So, the value of √i is (1/√2) + (1/√2)i.