Why do we use i to represent phasors and/or vectors?

In summary, the convention of representing vectors with a real and imaginary component (e.g. <3,4> as 3 + 4i) likely originated from the use of complex numbers and later quaternions. When working with wave phasors, the "i" term plays a crucial role in performing calculations and superimposing multiple waves.
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Somestimes, vectors (e.g <3,4>) are represented with a real and imaginary component (3 + 4i). When expressing wave phasors as vectors, this is usually the convention.

Insofar as phasors and waves go, what rationale does the convention have? If I had to superimpose two waves together, and perform an assortment of calculations, what role would the "i" term carry?
 
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I think the convention came from complex numbers use of i and then when quaternions were the rage the notion of i, j, k was used and later when vectors became more popular the real part was dropped and just the i, j, k remained.
 
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Related to Why do we use i to represent phasors and/or vectors?

1. Why is the letter "i" used to represent phasors and/or vectors?

The letter "i" is used to represent phasors and/or vectors because it is the standard mathematical notation for the imaginary unit, which is defined as the square root of -1. Phasors and vectors often involve complex numbers, and the imaginary unit is essential for representing and manipulating these numbers.

2. Is there a specific reason why "i" was chosen over other letters or symbols?

Yes, the letter "i" was chosen because it is the first letter of the word "imaginary," which reflects its role in representing the imaginary unit. Additionally, the letter "i" is commonly used in mathematics and physics to represent imaginary numbers, so it was a natural choice for representing phasors and vectors.

3. Are there any alternative symbols that can be used to represent phasors and/or vectors?

Yes, there are alternative symbols that can be used, such as "j" or "k," which are also commonly used to represent the imaginary unit. In electrical engineering, "j" is often used instead of "i" to represent the imaginary unit, as "i" is typically used to represent current. However, "i" remains the most widely used symbol for representing phasors and vectors.

4. What is the connection between phasors, vectors, and the imaginary unit?

Phasors and vectors are closely related to the imaginary unit because they both involve complex numbers. Phasors are used to represent the magnitude and phase of a sinusoidal function, while vectors are used to represent both magnitude and direction. The imaginary unit is essential for representing and manipulating these complex numbers in both phasors and vectors.

5. Can phasors and/or vectors be represented without using "i"?

Technically, yes, phasors and vectors can be represented without using "i." However, using "i" to represent the imaginary unit makes the representation and manipulation of these numbers much more straightforward and efficient. Additionally, "i" has become the standard notation for representing phasors and vectors, so using alternative symbols may cause confusion or misunderstandings.

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