# Can a phasor have a negative magnitude?

• Vishera
In summary, when describing a phasor, it is preferred to write the magnitude as positive and use a sign to indicate the angle. Both ##60\angle 10°## and ##60\angle 190°## are correct representations of the phasor and have equivalent magnitudes of 60. It is important to note that magnitude is always positive, and the angle can be described using a sign. Additionally, when calculating the direction of a phasor, it is important to use the four-quadrant version of the arctangent function, atan2(y,x), to ensure accuracy. Finally, while it may be tempting to use a negative magnitude as a mental aid, it is important to eventually break this habit and use
Vishera

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

They are both correct. They are both equal.

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.

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.

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

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

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## 1. Can a phasor have a negative magnitude?

Yes, a phasor can have a negative magnitude. Phasors are complex numbers that represent the amplitude and phase of a sinusoidal wave. The magnitude of a phasor is the length of the vector, and it can be positive or negative depending on the direction of the vector.

## 2. What does a negative magnitude of a phasor indicate?

A negative magnitude of a phasor indicates that the vector is pointing in the opposite direction of the positive axis. This means that the amplitude of the wave is negative, which can represent a phase shift of 180 degrees.

## 3. How is a negative magnitude of a phasor represented graphically?

A negative magnitude of a phasor is represented graphically by a vector pointing in the opposite direction of the positive axis. This vector will have the same length as a positive magnitude vector, but it will be pointing in the opposite direction.

## 4. Can a negative magnitude of a phasor affect the frequency of a wave?

No, the magnitude of a phasor does not affect the frequency of a wave. The frequency of a wave is determined by the rate at which it repeats over time and is not affected by the direction or amplitude of the phasor.

## 5. Are there any practical applications of phasors with negative magnitudes?

Yes, phasors with negative magnitudes have practical applications in electrical engineering and signal processing. They can be used to represent alternating current (AC) circuits, where the negative magnitude represents the phase shift between the voltage and current. They are also used in telecommunications and audio signal processing to represent phase differences between signals.

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