- #1

e101101

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- Homework Statement
- Hi there,

I'm currently taking an Optics course and the teacher is expecting us to have an understanding of the complex representation of waves. Although, hardly any of us have even heard of this yet. I've tried to google how to convert a cos(obj) and sin(obj) to an exponential... but I just don't understand. I would really love it if someone could explain this to me, as this has been really been bringing me down.

- Relevant Equations
- E=Eoexp[k•r±⍵t]

**Homework Statement:**Hi there,

I'm currently taking an Optics course and the teacher is expecting us to have an understanding of the complex representation of waves. Although, hardly any of us have even heard of this yet. I've tried to google how to convert a cos(obj) and sin(obj) to an exponential... but I just don't understand. I would really love it if someone could explain this to me, as this has been really been bringing me down.

**Homework Equations:**E=Eoexp[k•r±⍵t]

This is an equation we saw in class today:

E=Eocos[k•r±⍵t] (where E, Eo, k and r are vectors). The answer was given to us (equation above), but I really want to understand why that is the result.

What would the complex representation of this function be? Could you please be thorough with your explanation... I am so lost and need a clear (and simple) answer.

Also, how would this result change if there was a constant in the argument of the cos function (ex: phase constant)? What if this was a sine function (I know you can switch any sine function to a cos, but I would like to know how to do it the 'hard' way?