Magnitude of Exponential Function e^jθ 如何求e^jθ的大小/絕對值

How to find the magnitude of exponential function e^iθ? Or |e^iθ| = ?

According to Euler's formula,

e^iθ = cosθ + isinθ

To find the magnitude of |e^iθ|,

|e^iθ| = SQRT(e^iθ) = SQRT(cos²θ + isin²θ) = SQRT(1) = 1

Therefore,

the magnitude of e^iθ is 1.

In other words, the magnitude of complex exponential is 1.

Related Information:

Euler's formula 歐拉公式
Why is the magnitude of e^(jwt) equal to 1?
Absolute value of complex exponential