Propagation constant and its components:
The propagation constant of an electromagnetic wave in a medium is a complex number that represents the rate at which the wave's amplitude and phase change as it propagates through the medium. It consists of two components: the real part, which represents the attenuation of the wave, and the imaginary part, which represents the phase shift of the wave.

Given that the propagation constant is k = 2 + 3i, we can separate the real and imaginary parts as follows:
- The real part of k, Re(k), is 2.
- The imaginary part of k, Im(k), is 3.

Understanding the ratio of wavelength to skin depth:
The ratio of the wavelength in a medium (λ) to the skin depth (δ) is an important parameter in the study of electromagnetic wave propagation. The skin depth is a measure of how deeply an electromagnetic wave can penetrate into a conducting medium. It represents the distance over which the amplitude of the wave decreases by a factor of 1/e (approximately 37%).

To calculate the ratio, we need to determine the values of λ and δ. The skin depth is given by the formula:
δ = √(2/μσ),
where μ is the permeability of the medium and σ is its conductivity.

Since the question does not provide the values of μ and σ, we cannot calculate the exact values of λ and δ. However, we can still discuss the relationship between them using the given information.

Impact of the imaginary part of k on the ratio:
The imaginary part of the propagation constant, Im(k), represents the phase shift of the wave. It affects the wavelength in the medium, λ, by introducing a complex exponential term in the wave equation. This term leads to a change in the phase of the wave as it propagates through the medium.

Since the question does not provide the value of the frequency of the wave or any other relevant parameters, we cannot determine the exact impact of Im(k) on the ratio. However, we can say that the ratio of λ to δ will be affected by the imaginary part of k, as it influences the phase shift of the wave.

Conclusion:
In conclusion, the given information about the propagation constant, k = 2 + 3i, allows us to understand the real and imaginary parts of the constant. However, without additional information about the frequency, permeability, and conductivity of the medium, we cannot calculate the exact ratio of the wavelength to the skin depth.