Science:Math Exam Resources/Courses/MATH152/April 2015/Question A 22
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Question A 22 

Let . Write in the form with and real numbers with no unevaluated trigonometric function values. Hint: first write in polar form. 
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 

Recall that the polar form of a complex number is , where and . According to Euler's formula, , so we have that Try to find this . 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We write in polar form. To do this, we first compute the modulus of , which is Therefore (as reviewed in the hint), we have for some that We need to find an angle such that and Evidently, works. We then have Raising both sides to the fifth power gives and both and are equal to This gives a result of Remark: We could have also found a value for by taking , which in this case gives also. 