Why cos(i) Is Bigger Than 1 (and It’s Not a Mistake)

Описание: Why does cos(i) come out bigger than 1?

In real numbers, cosine is always between −1 and 1.
So how can cos(i) ≈ 1.543 be possible?

In this video, we explore what really happens when the cosine function receives a complex input. Using Euler’s formula, hyperbolic functions, and complex-plane visualizations, you’ll see why cosine is no longer a rotation — it becomes hyperbolic growth.

We break down:
• Why cos(i) = cosh(1)
• How imaginary inputs change cosine’s geometry
• Why cos²(i) + sin²(i) = 1 still works
• How vertical and horizontal lines transform into hyperbolas and ellipses
• What “hyperbolic” really means in complex analysis

This isn’t a paradox — it’s a deep geometric insight into complex functions, conformal mapping, and Euler’s identity.

If you’ve ever wondered:
– Why cosine exceeds 1
– Why imaginary numbers behave differently
– How trigonometry extends into the complex plane

…this video is for you.

🧠 Topics Covered
complex cosine
cos(i) explained
hyperbolic cosine
Euler’s formula
complex analysis visualization
conformal mapping
cosh and sinh
imaginary numbers
complex plane transformation

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