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Math Help - Computing an equation with polar form?

  1. #1
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    Computing an equation with polar form?

    "Compute |(2 + i)(cos(pi/6) - isin(pi/6))|"
    With trying to answer this question, I first converted (2+i) to polar form (I got √3(cos(pi/3) - isin(pi/3) - I'm not sure if that's correct) so, I then had both in polar form. Afterwards, I multiplied the two and was left with an answer that did not match the correct answer (√5). My answer was still in polar form so, I'm unsure if that was an incorrect approach or just a mistake with my working out. Moreover, does having "|" outside the equation, change or mean anything to how you're supposed to solve it?
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  2. #2
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    Quote Originally Posted by cottontails View Post
    "Compute |(2 + i)(cos(pi/6) - isin(pi/6))|"
    With trying to answer this question, I first converted (2+i) to polar form (I got √3(cos(pi/3) - isin(pi/3) - I'm not sure if that's correct) so, I then had both in polar form. Afterwards, I multiplied the two and was left with an answer that did not match the correct answer (√5). My answer was still in polar form so, I'm unsure if that was an incorrect approach or just a mistake with my working out. Moreover, does having "|" outside the equation, change or mean anything to how you're supposed to solve it?
    Here are several considerations.
    Are you sure you have the problem written correctly?
    Could it be 2+2\mathif{i}~?
    Because \arctan\left(\frac{1}{2}\right)\ne\frac{\pi}{3}. It is no nice value.
    Also |2+\mathif{i}|=\sqrt{5} not \sqrt{3}.

    Check the statement again.
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  3. #3
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    Quote Originally Posted by cottontails View Post
    "Compute |(2 + i)(cos(pi/6) - isin(pi/6))|"
    With trying to answer this question, I first converted (2+i) to polar form (I got √3(cos(pi/3) - isin(pi/3) - I'm not sure if that's correct) so, I then had both in polar form. Afterwards, I multiplied the two and was left with an answer that did not match the correct answer (√5). My answer was still in polar form so, I'm unsure if that was an incorrect approach or just a mistake with my working out. Moreover, does having "|" outside the equation, change or mean anything to how you're supposed to solve it?
    To add to Plato's comments: If you plot z = 2 + i on an Argand diagram (and when finding the polar form you should always do this) it should be crystal clear that 2 + i cannot possible be the same as √3(cos(pi/3) - isin(pi/3) - your polar form is not even in the correct quadrant (it is in the 4th quadrant!)
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