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I hope I am posting this is in the right section. It is not a home work question, it is from a solution to a tutorial, and I just cannot see how the lecturer has gotten from one step to the next. If I don't get the solution here, I will ask him, but that will be later next week, and I would like to understand it now.

Anyway. It is a question relating to a digital signal processing class, and we were asked to show analytically that

w(t) = r cos(100t+∅).

In the question, we are told that x(t) = cos(100t) and y(t) = cos(100t + [itex]\pi[/itex]) where w(t) = x(t) + y(t).

The part I am having an issue with is from this line

2w(t) = e^{j100t}+ e^{-j100t}+ e^{j100t + pi/3}+ e^{-j100t - pi/3}

To this line

2w(t) = e^{j100t}(e^{jpi/3}+1) + e^{-j100t}(e^{-jpi/3}+1)

I am sure it is a pretty basic step, but I just cannot see it, and I have no issues with other harder sections, but this is just a mental block for me.

Thanks in advance for any help you can gove me.

Seán

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# A little help understanding how you get from one step to the next

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