What are the components of the vector between the origin and the polar coordinate (-2, (3pi)/2)?

1 Answer
Topscooter
Jan 7, 2016

(0,-2).

Explanation:

I suggest to use complex numbers to solve this problem.
So here we want the vector 2e^(i(3pi)/2) = 2e^(i(-pi)/2.

By the Moivre formula, e^(itheta) = cos(theta) + isin(theta). We apply it here.

2e^(i(-pi)/2) = 2(cos(-pi/2) + isin(-pi/2)) = 2 (0 - i) = -2i.

This whole calculus was unnecessary though, with an angle like (3pi)/2 you easily guess that we will be on the (Oy) axis, you just see wether the angle is equivalent to pi/2 or -pi/2 in order to know the sign of the last component, component that will be the module.

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