SOLUTION: Write the complex number in polar form. -1/8 - 1/8i

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Question 1204946: Write the complex number in polar form.
-1/8 - 1/8i
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
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Write the complex number in polar form.
-1/8 - 1/8i
~~~~~~~~~~~~~~~~~~~~~~~ 

The point is in quadrant III, QIII.

The module is  r = sqrt%28%28-1%2F8%29%5E2%2B%28-1%2F8%29%5E2%29 = sqrt%281%2F64%2B1%2F64%29 = sqrt%282%2F64%29 = sqrt%282%29%2F8.

The argument is  tan%28theta%29 = %28%28-1%2F8%29%29%2F%28%28-1%2F8%29%29 = 1.


Therefore, the angle (the argument) is  theta = 5pi%2F4,  or  135 degrees.


So, the polar form for the point is  (r,theta) = (sqrt%282%29%2F8,5pi%2F4). 


The complex number in polar form is  z = %28sqrt%282%29%2F8%29%2A%28cos%285pi%2F4%29+%2B+i%2Asin%285pi%2F4%29%29.

Solved.