# Negative of Polar Coordinates

1. Nov 6, 2014

### Physicist3

Hi,

Say I have a variable 'x' which has the polar value 10@-75°, would '-x' be -10@+75° or 10@+75° as I am a touch confused as to which bit I have to invert

2. Nov 6, 2014

### slider142

The notation "-x" usually refers to the additive inverse of x. That is, we want x + (-x) = 0. Therefore, if you are using the usual Euclidean notion of vector addition (the parallelogram law, equivalent to the addition of Cartesian components), you must find the polar components of the vector whose addition to x will yield the additive identity: the 0 vector. In the vectors of Euclidean geometry, this is the vector that points in opposite direction to x, but with equal magnitude. Thus, it is the reflection of x through the origin (if one attaches the tail of x to the origin). Attached is an example of the geometric viewpoint. Do you see which vector that should be for your particular case ? After you find it geometrically, then you would find its polar components.
Of course, if you are using a different notion of vector addition, then your result will vary. In that case, you would have to describe the context of your application.

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Last edited: Nov 6, 2014
3. Nov 6, 2014

### mathman

In polar coordinates x and -x have the same magnitude and have angles which differ by 180 deg. In your example -x is 10@105 deg.