Search results
Results from the WOW.Com Content Network
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. Re is the real axis, Im is the imaginary axis, and i is the "imaginary unit", that satisfies i 2 = −1.
Substituting r(cos θ + i sin θ) for e ix and equating real and imaginary parts in this formula gives dr / dx = 0 and dθ / dx = 1. Thus, r is a constant, and θ is x + C for some constant C. The initial values r(0) = 1 and θ(0) = 0 come from e 0i = 1, giving r = 1 and θ = x.
In atmospheric applications, refractivity is defined as N = n – 1, often rescaled as either [60] N = 10 6 (n – 1) [61] [62] or N = 10 8 (n – 1); [63] the multiplication factors are used because the refractive index for air, n deviates from unity by at most a few parts per ten thousand.