Q. The value of $1 + i^{2} + i^{4} + i^{6} + \ldots + i^{2n}$ is
A) Positive
B) Negative
C) Zero
D) Cannot be determined
Explanation
(d)
Let $S = 1 + i^{2} + i^{4} + i^{6} + ... + i^{2n}$
$= 1 - 1 + 1 - 1 + 1 - ... + ( - 1)^{n}$
The value of $S$ depends on $n$
$\therefore\$The value cannot be determined
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.