Do the operation and express the answer in a + bi form. $\frac { 13 } { i ^ { 31 } }$
A) $13 i$
B) $- 13$
C) 13
D) $- 65 i$
E) $- 13 i$

Question

Quizplus · Accepted Answer

To solve $\frac { 13 } { i ^ { 31 } }$, we first simplify the denominator. Since $i^4 = 1$, $i^{31} = i^{28} \cdot i^3 = 1 \cdot i^3 = i^3 = -i$. Therefore, the expression becomes $\frac { 13 } { -i }$. Multiplying the numerator and the denominator by $i$ to get rid of the imaginary unit in the denominator, we get $\frac { 13i } { -i^2 }$. Since $i^2 = -1$, this simplifies to $\frac { 13i } { -(-1) } = 13i$.

Do the Operation and Express the Answer in a 13i31\frac { 13 } { i ^ { 31 } }i3113​

Do the Operation and Express the Answer in a $\frac { 13 } { i ^ { 31 } }$