Find the possible value(s) of 1/in, where i=-1 and n is an even positive integer.

GATE 2026 PI – Question 16

Engineering Mathematics · Linear Algebra · 1 mark · Multiple choice

Find the possible value(s) of $1/i^n$, where $i=\sqrt{-1}$ and n is an even positive integer.

Show answer and explanation

Correct answer: (A) $+1$ or $-1$

For n = 2k, $i^n=(i^2)^k=(-1)^k$. Its reciprocal is likewise $(-1)^k$, giving +1 for even k and −1 for odd k. **A**.

GATE 2026 PI Q38 – Match the matrices P,Q,R,S to properties 1: singular; 2: triangular; 3: symmetric; 4:…
GATE 2025 PI Q11 – Find the eigenvalues of A=pmatrix0&-1\\1&0pmatrix.
GATE 2024 PI Q36 – A=pmatrixa&b\&-apmatrix. If A² = I, which equation is true?
GATE 2023 PI Q49 – For A=pmatrix4&2\\3&3pmatrix, find the eigenvalue associated with eigenvector…
GATE 2022 PI Q11 – For vectors a,b,c, find ( a b) c.
GATE 2022 PI Q23 – A=pmatrix3\\2pmatrixpmatrix1&4pmatrix. Find det(A), rounded to nearest integer.