Final answer:
In the trigonometric form of a complex number, tanθ represents the ratio of the imaginary part to the real part of the complex number, which is tanθ = b/a.
Step-by-step explanation:
In the trigonometric form of the complex number z = a + bi, where a is the real part and b is the imaginary part, we can represent z in polar coordinates as r(cos θ + i sin θ), where r is the magnitude of z and θ is the argument or angle.
To find tanθ in terms of a and b, we consider the right triangle formed by the real and imaginary components of z. According to this right triangle,
tanθ = θ = opposite/adjacent = b/a
Therefore, in the context of a complex number in trigonometric form, tanθ represents the ratio of the imaginary part to the real part of the complex number, indicating the slope of the line connecting the origin to the point representing the complex number in the complex plane.