$$i^{225}+{\left(-i\right)}^{60}+i^{83}$$

$$=i^{224}·i+{\left(-i\right)}^{60}+i^{80}·i^3$$

$$=i^{4·56}·i+i^{4·25}+i^{4·20}·i^3$$

$$=1·i+1+1·\left(-i\right)$$

$$=i+1-i$$