\sqrt{i} in polar form can be written as r(\cos \theta + i \sin \theta), where r is a real number and 0 \leq \theta \leq \frac{\pi}{2}. What is the measure of \theta (in degrees)?

i = (1,pi/2)

√i = (1,pi/4)

To find the measure of θ in degrees, we need to understand the complex number i in polar form.

The complex number i is defined as i = √(-1). In polar form, i can be written as i = r(cosθ + isinθ), where r is a real number, and θ is the angle that i makes with the positive real axis.

To find the value of θ in degrees, we can use the equation θ = arctan(b/a), where a and b are the real and imaginary parts of the complex number i, respectively.

In this case, a = 0 (since there is no real part) and b = 1 (since the imaginary part is 1). Therefore, we have θ = arctan(1/0).

However, arctan(1/0) is undefined since division by zero is not allowed. In the complex plane, we have multiple possible values for the argument (or angle) of i.

For convenience, we often define the principal value of the argument of i as θ = π/2. This means that in this context, when converting √i to polar form, we assign the angle θ as π/2.

Thus, the measure of θ in degrees is given by θ = (π/2) * (180/π) = 90 degrees.