Imaginary Coefficient Calculator

Formula

To calculate the Imaginary Coefficient:

\[ IC = \frac{Im}{|Z|} \]

Where:

\(IC\) is the imaginary coefficient
\(Im\) is the imaginary part of the complex number
\(|Z|\) is the magnitude of the complex number, given by \(\sqrt{a^2 + b^2}\)

Imaginary Coefficient Definition

An imaginary coefficient is a numerical factor that multiplies the imaginary unit in a complex number. For a complex number of the form \(a + bi\), the imaginary coefficient is \(b\). This coefficient represents the magnitude of the imaginary part and is used in various fields, including signal processing and control systems.

Example Calculation

Let's assume the following values:

Real Part (a) = 3
Imaginary Part (b) = 4

Step 1: Calculate the magnitude of the complex number:

\[ |Z| = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

Step 2: Calculate the imaginary coefficient:

\[ IC = \frac{4}{5} = 0.8 \]

The imaginary coefficient (IC) is 0.8.