(1) ${\mathrm{i}}^{4\mathrm{n}+3}$
(2) $i^{8n+85}$
(3) $i^{16n-14}$

Step 1 ：The problem is asking for the value of $i^{4n+3}$, where $i$ is the imaginary unit and $n$ is an integer.

Step 2 ：The imaginary unit $i$ is defined as $\sqrt{-1}$, and it has a cyclic property: $i^1=i$, $i^2=-1$, $i^3=-i$, and $i^4=1$. After $i^4$, the cycle repeats.

Step 3 ：Therefore, we can simplify $i^{4n+3}$ by using the cyclic property of $i$.

Step 4 ：The function first calculates the exponent $4n+3$, then it calculates the cyclic exponent by taking the modulus of the exponent and 4.

Step 5 ：The function then returns the value of $i$ to the power of the cyclic exponent.

Step 6 ：$i^{4n+3}$ returns $i$ if $4n+3$ is congruent to 1 modulo 4, -1 if $4n+3$ is congruent to 2 modulo 4, -$i$ if $4n+3$ is congruent to 3 modulo 4, and 1 if $4n+3$ is congruent to 0 modulo 4.

Step 7 ：$\boxed{{\displaystyle \text{The value of }{i}^{4n+3}\text{ is given by the function, which returns }i\text{ if }4n+3\text{ is congruent to 1 modulo 4, -1 if }4n+3\text{ is congruent to 2 modulo 4, -}i\text{ if }4n+3\text{ is congruent to 3 modulo 4, and 1 if }4n+3\text{ is congruent to 0 modulo 4.}}}$