Is this a typo? (Complex positions of input and output links)

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The discussion centers on a potential typo in a homework problem involving complex vector forms. Participants agree that a "j" is missing from the sine function in the equation. The consensus is that this omission constitutes a typographical error. Clarification is sought to confirm the accuracy of the original statement. Overall, the focus remains on identifying and correcting the typo in the mathematical expression.
EastWindBreaks
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Homework Statement


upload_2017-11-7_6-51-13.png


Homework Equations

The Attempt at a Solution


upload_2017-11-7_6-52-17.png

since they are in complex vector form, its missing a " j " on the sin() part, correct?
 

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I believe you have it correct. It looks like a typo to me.
 
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Charles Link said:
I believe you have it correct. It looks like a typo to me.
thank you
 
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Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
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