# How to separate wavenumber $k$ into real and imaginary parts?

Physics Asked by park ning on December 15, 2020

In $k^2 – frac{omega^2}{c_o^2} + (tau_{alpha} i omega)^{alpha} k^2 = 0$, $k$ is the wavenumber, $omega$ is angular frequency, others are constants. How can I separate the wavenumber $k$ into real and imaginary parts, $k = frac{omega}{c(omega)} – i alpha_k$,?

$k^2$ is easy and I assume you know how to expand that into its real and imaginary parts. As for $ln k^2$, use the fact that (the principal branch of) $ln(r e^{itheta}) = ln(r) + itheta$. So, if you can write $k^2$ in the form $r e^{itheta}$, you're done. Now, writing a complex number $a + i b$ in its polar form $r e^{itheta}$ isn't hard: $r = sqrt{a^2 + b^2}$ and $theta = arctan left( dfrac{b}{a} right)$.

Answered by wltrup on December 15, 2020

## Related Questions

### Potential below a grounded conducting plane

1  Asked on January 8, 2021 by ssw1004

### Fluid Mechanics Infinite Plate Assumption

0  Asked on January 8, 2021 by johz

### Explaining accelerating spacetime expansion?

0  Asked on January 8, 2021 by jonah-weinbaum

### How do photons carry information?

1  Asked on January 8, 2021 by manish-kumar-singh

### Proof of the differential Bianchi identity

2  Asked on January 8, 2021

### Why doesn’t a compression pulse on a spring move backwards?

1  Asked on January 8, 2021

### Huygens’ Principle alternative explanation on reflection

1  Asked on January 8, 2021 by lyle

### When to use Conservation of Energy vs Conservation of Momentum

2  Asked on January 8, 2021 by jo-p

### Published claimed falsifications of objective collapse theories

1  Asked on January 8, 2021

### Can liquids exert/be affected by normal force?

1  Asked on January 8, 2021 by eva

### Can the narrative of spooky action at a distance be derived from the mathematics of quantum mechanics?

0  Asked on January 8, 2021

### Big crunch theory

1  Asked on January 8, 2021 by kawaljeet-kaur

### How to define temperature in non-equilibrium, non-thermodynamic systems?

2  Asked on January 8, 2021 by honeste_vivere

### Boundary conditions for an imperfect conductor

3  Asked on January 8, 2021 by joshua-benabou

### Does work done depend on the frame of reference?

7  Asked on January 8, 2021 by user167102

### Hydrogen atom in quantum field theory

1  Asked on January 8, 2021 by peter-a

### How can a coil self-induce voltage at $t=0$?

1  Asked on January 8, 2021 by fihdi

### Maxwell Stress Tensor at material boundaries

1  Asked on January 8, 2021 by fork2