I'm reading a book about the `sqrt(-1)`  however I am running into symbols that I don't recognize and it makes the book much more confusing.  These are the symbols; `θ x ̂ x ̅ f' (x)` ``I...

I'm reading a book about the `sqrt(-1)`  however I am running into symbols that I don't recognize and it makes the book much more confusing. 

These are the symbols; `θ x ̂ x ̅ f' (x)`

``I don't know if that showed up properly so I'm going to tell you what they look like. the 1st one looks like a zero with a line through it sideways, the next is an x with a line overtop of it, the third is an x with ^ over top of it, and the final one looks like its f(x) which I know equals y, but this seems to act differently, it is f'(x).

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rakesh05's profile pic

rakesh05 | High School Teacher | (Level 1) Assistant Educator

Posted on

Because you are talking about complex numbers. So as per your question I would like to explain one by one.

Let us consider a complex number `z` which is can be written as

`z=x+iy` , here the  `i`  separates the imaginary part `y` of the complex number `z` from its real part `x` . Here `i=sqrt(-1).`

The modulus or magnitude of the complex number `z` is equal to `sqrt(x^2+y^2)` .

And the argument of the complex number `z`  is the angle made by the line joining the number `z` in the complex plane to the origin with positive direction of x-axis. The angle measured is in positive sense.

So the first thing you asked is `theta` , which is the argument of the complex number `z.`   

Because  in order to represent a complex number we also use vector notation. So  `hatz` ``   denote the unit vector in the direction of the vector `z.` This is the answer for your second thing.

The complex conjugate of the complex number `z=x+iy`  is `barz=x-iy` . So `barz` denote the complex conjugate of the complex number `z.` This is the answer for your third query.

Finaly if we talk about a function as  `y=f(x).` The derivative of the function `y=f(x) ` with respect to `x`  is     `dy/dx=d/dx{f(x)}`

 This `d/dx{f(x)}` is also denoted by `f'(x).` So in case of functions

this  `f'`  denote the first derivative of the function. This is the answer for youe last doubt.

 

 

 

embizze's profile pic

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The symbols you asked about are `theta, hat(x), bar(x),f'(x)` :

The first is probably the greek letter theta -- often used to name an angle. Since `i=sqrt(-1)` is used to describe rotations in the complex plane, I imagine this is the context that it is used. e.g. `e^(i theta)=costheta+isintheta`

The second is usually read x-hat in mathematics. It might be describing a unit vector ( a vector with magnitude 1), especially if you are looking at vectors in the complex plane. However, it is also used as an estimator. In the book "An Imaginary Tale The Story of `sqrt(-1)` " by Paul J. Nahin, `hat(x)` is used in the first chapter to describe a particulr x-coordinate, so it is just a way to indicate that it is not the variable x.

The third is read x bar, and usually indicates the arithmetic mean (average) of a set of numbers. I'm not sure of the context that you would be encountering it.

The last is the derivative of the function f(x). This describes the rate of change of a variable. (In physics, the velocity is the rate of change of position, and the velocity function is the first derivative of the position function.) You would need to take a calculus course to fully understand.

Depending on what book you are reading, you are apt to encounter a wide range of symbols as i is used in a number of fields.

romanceluver22's profile pic

romanceluver22 | Student, Grade 11 | (Level 1) eNoter

Posted on

Thank you guys all for answering it was very helpful! And I may run into more of these symbols soon so look for them! 

romanceluver22's profile pic

romanceluver22 | Student, Grade 11 | (Level 1) eNoter

Posted on

The symbols you asked about are :

The first is probably the greek letter theta -- often used to name an angle. Since is used to describe rotations in the complex plane, I imagine this is the context that it is used. e.g.

The second is usually read x-hat in mathematics. It might be describing a unit vector ( a vector with magnitude 1), especially if you are looking at vectors in the complex plane. However, it is also used as an estimator. In the book "An Imaginary Tale The Story of " by Paul J. Nahin, is used in the first chapter to describe a particulr x-coordinate, so it is just a way to indicate that it is not the variable x.

The third is read x bar, and usually indicates the arithmetic mean (average) of a set of numbers. I'm not sure of the context that you would be encountering it.

The last is the derivative of the function f(x). This describes the rate of change of a variable. (In physics, the velocity is the rate of change of position, and the velocity function is the first derivative of the position function.) You would need to take a calculus course to fully understand.

Depending on what book you are reading, you are apt to encounter a wide range of symbols as i is used in a number of fields.

 

I am actually reading the book that you talked about, "An Imaginary Tale The Story of  " by Paul J. Nahin, and have been running into these symbols. For the x bar I actually put the x in place of the various numbers that I saw with that bar above it. 

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