Science:Math Exam Resources/Courses/MATH152/April 2016/Question B 05 (c)
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Question B 05 (c) 

Consider . Recall that . (c) Write in polar form. That is, find a real number and such that . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

In the polar form of a complex number , two variables and are determined by the relations

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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. For any complex number , we have and . We know from part (b) that We also have . We are given that . From part (a), is in the second quadrant, which is consistent with a negative tangent. So we know that must form an angle of with the axis and lie in the second quadrant. We also require that . Hence Therefore, the desired polar form is . 