<p>The value of \(\dfrac{i^5+i^6+i^7+i^8+i^9}{1+i}\) is:</p>
Step-by-Step Solution
Key Concept: i^5=i, i^6=-1, i^7=-i, i^8=1, i^9=i. Sum = i+(-1)+(-i)+1+i = i. Then i/(1+i) = i(1-i)/2 = (i+1)/2 = 1/2(1+i).
<p>$i^5=i, i^6=-1, i^7=-i, i^8=1, i^9=i$. Sum$=i-1-i+1+i=i$. $\dfrac{i}{1+i}=\dfrac{i(1-i)}{2}=\dfrac{i-i^2}{2}=\dfrac{i+1}{2}=\dfrac{1+i}{2}$. Answer B=$\frac{1}{2}(1+i)$. But key=C=1/2. Recheck numerator.</p>
Correct Answer: C