Simplify the power of i.
-$$\frac { 1 } { \mathrm { i } ^ { 51 } }$$
A) $- \mathrm { i }$
B) $\mathrm { i }$
C) 1
D) $- 1$

Question

Quizplus · Accepted Answer

The powers of $i$ cycle through a pattern: $i^1 = i$, $i^2 = -1$, $i^3 = -i$, $i^4 = 1$, and then it repeats. $i^{51}$ can be simplified by dividing 51 by 4, which gives a remainder of 3. Therefore, $i^{51} = i^3 = -i$. Thus, $\frac{1}{i^{51}} = \frac{1}{-i} = i$, because multiplying numerator and denominator by $i$ gives $\frac{i}{-i^2} = \frac{i}{1} = i$.

Simplify the Power of I 1i51\frac { 1 } { \mathrm { i } ^ { 51 } }i511​

Simplify the Power of I $\frac { 1 } { \mathrm { i } ^ { 51 } }$