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  "body": "\n## Proof\n\n1. Let $\\pi$ be the real number [[pi|0C1VYVNV2N]].\n2. Apply [[Euler's formula|04R3CY41VJ]] with $z = \\pi$: $e^{i \\pi} = \\cos \\pi + i \\sin \\pi$.\nFor the real number $\\pi$, these power series are the real [[sine and cosine|0WB57D9488]].\n3. By [[cos pi = -1|01A8JGR4JM]], $\\cos \\pi = -1$ and $\\sin \\pi = 0$. So $e^{i \\pi} = -1 + 0 i = -1$.\n4. Adding $1$ to both sides gives $e^{i \\pi} + 1 = 0$.\n\n## Idea\n\nEuler's formula turns $e^{i \\pi}$ into the point of the unit circle at angle $\\pi$.\nThat point is $-1$, half a turn from $1$.\n",
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