What is Euler’s Formula?

Euler’s Formula is a fundamental equation in complex analysis that establishes the deep relationship between trigonometric functions and the complex exponential function. It is expressed as e^(iθ) = cos(θ) + i·sin(θ), where e is the base of natural logarithms, i is the imaginary unit, and θ is the angle in radians. This formula provides a powerful way to represent complex numbers and is widely used in various fields of mathematics, physics, and engineering.

How to Use the Euler’s Formula Calculator

Step 1: Enter the angle

Input the angle θ in radians into the provided field. This value can be any real number, including decimals.

Step 2: Click “Calculate”

Press the “Calculate” button to process your input. The calculator will use Euler’s formula to compute the result.

Step 3: Interpret the results

The calculator will display the result in the form a + bi, where ‘a’ is the real part (cosine of the angle) and ‘b’ is the imaginary part (sine of the angle). Both values are rounded to four decimal places for clarity.

Step 4: Read the explanation

Below the result, you’ll find a brief explanation of how the calculation was performed and what the numbers represent. This helps in understanding the relationship between the input angle and the complex number output.