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## Homework Statement

For my waves class, I have to do this problem. I've previously completed a question like this except there was no phase constant (∏/4) in that question.

Express the following in the form x = Re [Ae^i[itex]\alpha[/itex]e^iwt

x=cos(wt + ∏/4) - sin(wt)

## Homework Equations

euler's formula e^iwt = cos(wt) + isin(wt)

complex amplitude = √A

^{2}+B

^{2}

complex angle = tan [itex]\alpha[/itex] = y/x

## The Attempt at a Solution

I know that cos(wt + ∏/4) = Re [e^i(wt + ∏/4)] and -sin(wt) = Re [ie^iwt]

combining these two, i have Re [e^i(wt + ∏/4) + ie^iwt] which, after factoring, becomes

Re [e^iwt (e^i∏/4 + i)]

My problem is, what do i do with the e^i∏/4 to get the complex amplitude and complex angle? In my previous problem without the ∏/4 shift, i was able to plot in Cartesian coordinates Im vs Re and successfully convert to polar coordinates. Help?