Introduction:
The value of √i refers to the square root of the imaginary unit i. To find the value of √i, we need to understand the properties of complex numbers and the concept of square roots in the complex number system.

Understanding Complex Numbers:
Complex numbers are numbers that have both a real part and an imaginary part. They are expressed in the form a + bi, where "a" represents the real part and "bi" represents the imaginary part. The imaginary unit i is defined as the square root of -1.

Finding the Square Root of i:
To find the square root of i, we need to express i in exponential form. The exponential form of a complex number z is given by z = re^(iθ), where r is the magnitude of z and θ is the argument of z.

Expressing i in Exponential Form:
i can be expressed as i = 1e^(iπ/2), where 1 is the magnitude and π/2 is the argument. This is because e^(iπ/2) equals i according to Euler's formula: e^(iθ) = cos(θ) + i sin(θ).

Calculating the Square Root:
Now, let's find the square root of i by using the exponential form of i. We need to find a complex number z = re^(iθ) such that z^2 = i.

1. Expressing the Square Root of i:
We can express the square root of i as √i = (re^(iθ))^(1/2).

2. Applying the Exponent Rule:
Using the exponent rule, we can rewrite the square root as (√r)e^(iθ/2).

3. Calculating the Magnitude:
The magnitude of the square root is √(√r), which simplifies to √(√1) = 1.

4. Calculating the Argument:
The argument of the square root is (θ/2), which is (π/2) / 2 = π/4.

5. Expressing the Square Root of i (Final Answer):
Therefore, the value of √i is (√1)e^(iπ/4), which simplifies to 1e^(iπ/4).

Conclusion:
The value of √i is 1e^(iπ/4) in exponential form. This represents a complex number with a magnitude of 1 and an argument of π/4.