Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am having trouble understanding how $10jy$ is converted to $10 e^{j\pi/2}$. Here $x$ and $y$ are unit vectors:

(original image)

$$\large=\operatorname{Re}\left[(10\hat{x}-10j\hat{y})e^{-j10\pi z}e^{jwt}\right]$$ $$\large=\operatorname{Re}\left[(10\hat{x}-10e^{j\pi/2}\hat{y})e^{-j10\pi z}e^{jwt}\right]$$ $$\large=\underbrace{10\hat{x}\cdot\cos(\omega t-10\pi z)}_{Ex}+\underbrace{10\hat{y}\cos(\omega t-10\pi z-\tfrac{\pi}{2})}_{Ey}$$

Thank you.

share|improve this question
add comment

1 Answer

up vote 2 down vote accepted

Euler's formula says that for any $\theta$, $$e^{j\theta}=\cos(\theta)+j\sin(\theta).$$ Therefore, $$e^{j\pi/2}=\cos(\tfrac{\pi}{2})+j\sin(\tfrac{\pi}{2})=0+j\cdot 1=j$$ and thus $10j=10e^{j\pi/2}$ (or, if you want to talk about vectors, $10j\hat{y}=10e^{j\pi/2}\hat{y}$; but note that it is incorrect to say that $10j\hat{y}=10e^{j\pi/2}$, because the left side is a vector, and the right side is a scalar).

share|improve this answer
    
thanks ! I though that it was Euler's formula but got lost as there are many variations... –  Parhs Jun 18 '12 at 16:24
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.