# Can a phasor have a negative magnitude?

1. Mar 21, 2014

### Vishera

Would it be preferred to write $-60\angle 10°\quad or\quad 60\angle 190°?$

Would one or the other be incorrect? Those two phasors are equivalent, right?

2. Mar 21, 2014

### psparky

They are both correct. They are both equal.

3. Mar 21, 2014

### sophiecentaur

The 'magnitude' in each case is 60. Magnitude is always positive. The angle of the phasor can be described using a sign. So your post is correct but the answer to the title is no.

4. Mar 21, 2014

### Baluncore

Given the rectangular x and y components of a phasor, the direction is the Arctangent(y/x),
while magnitude = Sqrt(x*x + y*y). The square root of the sum of squares will never be negative.

5. Mar 22, 2014

### olivermsun

IIRC you need the four-quadrant version atan2(y, x) to get the phase.

6. Mar 22, 2014

### jim hardy

As Sophie indicated - you should form the habit of magnitude positive, angle where it falls.
That's just "how it's done".

to use a parallel from the dictionary -

Words like "irregardless" and "drownded" are in the dictionary but carry stylistic label "substandard", meaning not used by people considered educated.
Pronunciation of the word "nuclear" as "noo-kyu-ler" used to be labelled "substandard".
But after three US presidents used it, it was upgraded to "nonstandard" meaning "not correct but used by many people who are considered educated". The inference is they should know better.

Ever read that section in the front of Webster's, "Stylistic Labels" ? It's kinda fun.
Noo-kyu-ler might even be just an alternate pronunciation nowadays - it was 1970's last time i looked..

So use negative magnitude as an aid in your thinking until you no longer need it, just don't admit to it.

old jim

Last edited: Mar 22, 2014