This "Impossible" Power (-e)^π Isn't What You Think

What do you really get when you raise a negative number to a strange exponent like π? 🤔

At first glance, (−e)ᵖⁱ looks impossible in the real-number world.
A negative base, a non-integer exponent… surely that must be “undefined,” right?

In this video, we explore complex numbers, Euler’s formula, and polar form to reveal that (−e)ᵖⁱ is not only well-defined, but actually a very specific complex number.

🔹 Why (−e)ᵖⁱ seems impossible in ℝ
🔹 How writing −e = e^(1 + iπ) changes everything
🔹 Using e^(iθ) = cos θ + i sin θ to find its exact value
🔹 Geometric meaning on the complex plane (magnitude and angle)
🔹 How this connects to expressions like iⁱ

If you enjoy visual explanations, complex analysis, and “impossible” expressions that secretly make sense, this video is for you 💡

📌 Topics:
complex numbers, Euler’s formula, polar form, powers of e, powers of negative numbers, (−e)ᵖⁱ

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