Explanation
Quotient of $4  3i$ by its Conjugate
To find the quotient of the complex number $4  3i$ divided by its conjugate, follow these steps:

Identify the conjugate of the complex number $4  3i$.
The conjugate of $4  3i$ is $4 + 3i$.

Express the division as a fraction:
$\frac{4  3i}{4 + 3i}$ 
Multiply numerator and denominator by the conjugate of the denominator:
$\frac{(4  3i)(4  3i)}{(4 + 3i)(4  3i)}$ 
Calculate the numerator:
Expanding the terms:
$= 16  12i  12i + 9i^2$Since $i^2 = 1$:
$= 16  24i + 9(1) = 16  24i  9 = 7  24i$ Calculate the denominator:
Expanding the terms:
$= 16  12i + 12i  9i^2$Again, since $i^2 = 1$:
$= 16 + 9 = 25$
Express the final result:
$\frac{7  24i}{25} = \frac{7}{25}  \frac{24i}{25}$
Hence, the quotient of the complex number $\mathbf{4  3i}$ divided by its conjugate is:
$\boxed{\frac{7}{25}  \frac{24}{25}i}$In the context provided, this corresponds to the third option: $\mathbf{\frac{7}{25}  \frac{24}{25}i}$.