Enter the values of e, i, and π into the calculator to determine Euler’s Identity.

Euler’s Identity Formula

The following formula is used to calculate Euler’s Identity. 

e^{(iπ)} + 1 = 0

Variables:

  • e is the base of the natural logarithm (approximately equal to 2.71828)
  • i is the imaginary unit, which satisfies the equation i^2 = -1
  • π is the ratio of the circumference of a circle to its diameter (approximately equal to 3.14159)

To calculate Euler’s Identity, raise e to the power of i times π, then add 1. The result should always equal 0, as per the identity.

What is Euler’s Identity?

Euler’s Identity is a mathematical equation that combines five of the most important numbers in mathematics: 0, 1, pi, e (Euler’s number, approximately 2.71828), and i (the imaginary unit). The identity is expressed as e^(iπ) + 1 = 0. This equation is considered beautiful and profound because it links together several fundamental mathematical concepts: addition, multiplication, exponentiation, and equality.

How to Calculate Euler’s Identity?

The following steps outline how to calculate Euler’s Identity using the formula: e^(iπ) + 1 = 0.

  1. First, identify the variables in the formula:
  2. e: base of the natural logarithm (approximately equal to 2.71828)
  3. i: imaginary unit, satisfying the equation i^2 = -1
  4. π: ratio of the circumference of a circle to its diameter (approximately equal to 3.14159)
  5. Next, substitute the values of the variables into the formula: e^(iπ) + 1 = 0.
  6. Calculate e^(iπ) using the properties of exponents and trigonometry.
  7. Add 1 to the result of e^(iπ).
  8. Finally, check if the result is equal to 0. If it is, Euler’s Identity is confirmed.

Example Problem:

Use the following values as an example problem to test Euler’s Identity:

e: 2.71828

i: √(-1)

π: 3.14159