why |e^ja| equal to 1

[sna_gz]

what is the proof of this rule:

[math]\lvert e^{ja} \rvert = 1[/math]
where j is the imaginary and a is an ordinary real number

 

[BigBeachBanana]

In general, [imath]z=x+jy[/imath], and [imath]|z|=\sqrt{x^2+y^2}[/imath], for [imath]x,y \in \R[/imath] . Also, [imath]e^{ja}=\cos a +j\sin a [/imath].
Then [math]|e^{ja}|=\sqrt{\cos^2 a+\sin^2 a}=\sqrt{1}=1[/math]

 

[topsquark]

what is the proof of this rule:

[math]\lvert e^{ja} \rvert = 1[/math]
where j is the imaginary and a is an ordinary real number

Or [imath]|z| = | \sqrt{z^* z} |[/imath] where z = x + jy and [imath]z^*[/imath] is the complex conjugate. Then [imath]|e^{ja}| = | \sqrt{ e^{-ja} e^{ja} } | = | \sqrt{1} | = 1[/imath].

-Dan