Science:Math Exam Resources/Courses/MATH152/April 2011/Question A 20
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Question A 20 

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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

Representing a complex number in the plane; can you geometrically describe what are the values and ? 
Hint 2 

To follow on the previous hint:
See the Wikipedia entry for absolute value and argument of a complex number. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. The absolute value (or modulus) of a complex number is and the argument, , is the angle between the right side of the axis and the position of the complex number on the plane. In this case, the argument is . To see that, you can either just visually see that the point (1,1) is clearly on the diagonal of the second quadrant of the plane, or using trigonometry have and from there notice that the corresponding angle is (or in real life compute the angle using a calculator since you only know a very few values of sine and cosine). So this allows us to write our complex number in polar form as 