Question

$i+i^2+i^3+i^4+....+i^{100}$ equals:

• A. $-1$
• B. $0$
• C. $1$
• D. None

Answer 1

The correct option is B

$0$

Evaluating the given series

$i+i^2+i^3+i^4+....+i^{100}$

The power of $i$ follows a cyclicity of 4.

Checking up to four powers:

$$\begin{gathered} \Rightarrow i+i^2+i^3+i^4 \\ \Rightarrow i-1-i+1 \\ \Rightarrow 0 \end{gathered}$$

Therefore,

$$\begin{gathered} \Rightarrow i+i^2+i^3+i^4+....+i^{100} \\ \Rightarrow i+i^2+i^3+i^4[\text{upto 25 times}\because \raisebox{1ex}{$100$}\!\left/ \!\raisebox{-1ex}{$4$}\right.=25\text{]} \\ \Rightarrow 0 \end{gathered}$$

Hence, the correct answer is Option (B).