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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