1. The problem is to verify the identity $$e^{i \pi} + 1 = 0$$, which is known as Euler's formula. 2. Euler's formula states that for any real number $\theta$, $$e^{i \theta} = \cos(\theta) + i \sin(\theta)$$. 3. Applying this to $\theta = \pi$, we get: $$e^{i \pi} = \cos(\pi) + i \sin(\pi)$$. 4. We know that $\cos(\pi) = -1$ and $\sin(\pi) = 0$, so: $$e^{i \pi} = -1 + 0i = -1$$. 5. Substitute back into the original expression: $$e^{i \pi} + 1 = -1 + 1 = 0$$. 6. Therefore, the identity $$e^{i \pi} + 1 = 0$$ is true. This is a fundamental and beautiful equation in mathematics connecting exponential functions, complex numbers, and trigonometry.