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1 2 3 4 Viewing the point P from two directions in the complex plane P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers

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1 2 3 4 Separating the real P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers And the imaginary parts We have two unknowns And two scalar equations to solve for them

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1 2 3 4 Rearranging terms P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Squaring and adding

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1 2 3 4 Rearranging terms P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Rearranging further

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1 2 3 4 SubstituteSubstitute P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers AndAnd To get OrOr

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1 2 3 4 P O Re Im Q Position Analysis of a 4 bar RRRR Linkage Using Complex Numbers Solving we get two roots! Solving AndAnd The signs of sin 3 and cos 3 will let us determine the quadrant in which 3 lies

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