Complex Numbers: Euler's formula problem

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SUMMARY

The discussion centers on the application of Euler's formula in simplifying complex numbers, specifically using the expression zj = xj + iyj. The user successfully derived the expression Re(z2 + z1)cosθ + Im(z2 - z1)sinθ but questions its validity and whether other identities could yield a solution purely in terms of 'z'. The consensus among participants confirms that the derived expression is valid.

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WWCY
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Homework Statement


Screen Shot 2017-08-22 at 6.15.45 PM.png


Homework Equations

The Attempt at a Solution



I attempted to use the formula zj = xj + iyj to substitute both z's. Further simplification gave me (x1 + x2)cosθ + (y2 - y1)sinθ or, Re(z2 + z1)cosθ + Im(z2 - z1)sinθ.

Is this a valid answer? Or are there any other identities I should have used to obtain an answer purely in 'z'?

I don't seem to be able to reduce the problem into Acosθ + Bcosθ any other way.

Thanks in advance!
 
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WWCY said:
Re(z2 + z1)cosθ + Im(z2 - z1)sinθ.
Looks good to me.
 
haruspex said:
Looks good to me.

Thank you!
 

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