Let's say that there is a polar equation:
-2400 + 8320j
To convert this polar equation to phasor form, should the negative be considered when trying to find the angle?
Would the angle be +73.91 or -73.91?
I am confused because in my book they consider the negative, but I saw a solution on chegg where they use the positive convention...
Ok there are 4 different concepts you are confusing:
1) Vector
A vector is a multivalued field variable, often used for representing coordinates. Examples are $\begin {bmatrix} 1 & 1 \end{bmatrix}$, $\begin {bmatrix} 2 \\ 3.7 \end{bmatrix}$, $\begin {bmatrix} 0 & 0 & 0 & 0 & 0 \end{bmatrix}$. Those are two two dimensional vectors and one five dimensional vector.
2) Polar coordinate:
Polar coordinates are a way to represent a 2D location using 2 values, distance and angle. You can convert between 2D vectors and polar coordinates. Examples:
$$\sqrt{2} \angle 60^o$$ $$10 \text{ meters } \angle \frac 12 \text{ radians}$$
There are different ways of doing 3d polar coordinates like sphereical coordinates, but "polar form" by itself almost always means 2D.
3) Complex Number
Complex numbers are numbers that may involve $i = \sqrt{-1}$. Professionals with often use $j$ instead of $i$ because $i$ is used to represent current. They originally came about as solutions to polynomials. Examples:
$$10 + 4i$$ $$\sqrt{-4} = 2i$$ $$\text{the solutions of } x^2 + 9 = 0$$
4) Complex Number in Phasor Form
Phasors are complex numbers written as $e^X$, where $X$ is a complex number. They are used by DSP engineers (among others) to represent oscillations such as sound. All complex numbers can be converted to phasor form. Examples:
$$e^{\pi i}$$ $$e^{(2\pi At + B)i + \ln C}$$
The first is the phasor form of $-1$. The second is the phasor form of a signal with a frequency $A$, phase of $B$, and magnitude of $C$.
$-2400 + 8320j$ is a complex number. In a complex plane, it is in the top left quadrant, so it's angle is between $\frac 12 \pi$ and $\pi$ radians.
The vector which represents the coordinate of this complex number in a complex plane is $\begin{bmatrix} -2400 & 8320\end{bmatrix}$.
The polar form of the vector is found by solving a triangle:
With the Pythagorean theorem you can see that the length of the green line is $\sqrt{2400^2 + 8320^2}$ which is about $8660$. The blue angle $\theta$ is given by using a the tangent formula $\tan(\theta) = \frac{8320}{2400}$, so the angle is approximately $74$ degrees. The red angle is the angle we are interesting in, which is $180 - 74 = 106$ degrees. So your polar form is approximately:
$$8660 \angle 106^o$$
To convert from polar form to phasor form, use:
$$\text{Magnitude }\cdot e^{i \cdot \text{ angle}}$$
Phasors are always in radians. So your phasor form is:
$$8660 e^{i \cdot 106 \frac {\pi} {180}} = e^{i 1.85 + \ln 8660} = e^{1.85i + 9.07}$$
...approximately.