SOLUTION: Use DeMoivre's theorem to write in trigonometric from: (1/2 - i(√3)/2)

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Question 1039836: Use DeMoivre's theorem to write in trigonometric from:
(1/2 - i(√3)/2)
Found 2 solutions by Edwin McCravy, ikleyn:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

The complex number 1%2F2%2Bi%2Asqrt%283%29%2F2 is represented by
the vector (arrow) from the origin to the point. Its length
is r and its angle with the right side of the x-axis is q.

%28matrix%281%2C3%2C1%2F2%2C%22%2C%22%2Csqrt%283%29%2F2%29%29



We draw a perpendicular (in green) from the point to the
x-axis:



That makes a right triangle and we can use the
Pythagorean theorem:

r%5E2=%281%2F2%29%5E2%2B%28sqrt%283%29%2F2%29%5E2
r%5E2=1%2F4%2B3%2F4
r%5E2=4%2F4
r%5E2=1
r=1

And since we know that SINE=OPP%2FHYP,

sin%28theta%29=%28sqrt%283%29%2F2%29%2F1=sqrt%283%29%2F2
theta=%2260%B0%22 

So the trigonometric form of  1%2F2%2Bi%2Asqrt%283%29%2F2

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

1%28cos%28%2260%B0%22%29%2Bisin%28%2260%B0%22%29%5E%22%22%29

Or if yout teacher wants you to use radians, then 

%2260%B0%22=pi%2F3

1%28cos%28pi%2F3%29%2Bisin%28pi%2F3%29%5E%22%22%29.

Edwin

Answer by ikleyn(52786) About Me  (Show Source):