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

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Question 1150572: Write the complex number in polar form


-1-i
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The polar form of A+Bi is 

r%28cos%28theta%29%5E%22%22%2Bi%2Asin%28theta%29%5E%22%22%29

The complex number A+Bi is a vector (arrow) drawn from the point (0,0) to
the point (A,B).

So
The complex number -1-1i is a vector (arrow) drawn from the point (0,0) to
the point (-1,-1), which is this:



We draw the right triangle which has one leg on the x-axis and the other leg
(in green) perpendicular to the x-axis and ending at the point (-1,-1):



Then we calculate r, which is the length of the arrow, by the Pythagorean
theorem:



Then we find θ measured counter-clockwise and swung around from the right
side of the x-axis, indicated by the red arc:



Use the unit circle to find θ since it is a special angle.

So theta=225%5Eo=%285pi%29%2F4

The polar form for -1-i is 

r%28cos%28theta%29%2Bi%2Asin%28theta%5E%22%22%29%29

sqrt%282%29%28cos%28225%5Eo%29%5E%22%22%2Bi%2Asin%28225%5Eo%29%5E%22%22%29

if your teacher wants the angle in degrees, or

sqrt%282%29%28cos%28%285pi%29%2F4%29%5E%22%22%2Bi%2Asin%28%285pi%29%2F4%29%5E%22%22%29

if your teacher wants the angle in radians.

Edwin