Do the operation and express the answer in a + bi form. $\frac { 17 } { i ^ { 31 } }$
A)-17i
B)-85i
C)-17
D)17i
E)17

Question

Do the operation and express the answer in a + bi form.​ $\frac { 17 } { i ^ { 31 } }$ ​
A)-17i
B)-85i
C)-17
D)17i
E)17

Quizplus · Accepted Answer

To simplify the expression $\frac { 17 } { i ^ { 31 } }$, 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 $\frac { 17 } { -i }$. Multiplying the numerator and the denominator by $i$, we get $\frac { 17i } { -i^2 }$. Since $i^2 = -1$, this simplifies to $\frac { 17i } { 1 } = 17i$.

Do the Operation and Express the Answer in a 17i31\frac { 17 } { i ^ { 31 } }i3117​

Do the Operation and Express the Answer in a $\frac { 17 } { i ^ { 31 } }$