What is i^13 × i^22?

First reduce each power of $i$ using its remainder when the exponent is divided by $4$. Since $13=4(3)+1$, $i^{13}=i$. Since $22=4(5)+2$, $i^{22}=i^2=-1$. The product is $i\cdot(-1)=-i$, choice D. Alternatively, add the exponents: $i^{35}$, and $35=4(8)+3$, so $i^{35}=i^3=-i$. Choice A ($i$) drops the negative sign from $i^{22}$. Choice B ($-1$) and choice C ($1$) come from using wrong remainders. Each remainder of $0, 1, 2, 3$ gives a different power of $i$.