JEE Advanced · MathematicsEasy

$Find the value of i^{4 n + 3}, where n is a positive integer.$

A. $1$
B. $- 1$
C. $i$
D. $- i$

Show correct answer & step-by-step solution

Correct answer: D — $- i$

Solution

$The expression is i^{4 n + 3} = i^{4 n} \cdot i^{3} .$
$Since i^{4} = 1, we have i^{4 n} = (i^{4})^{n} = 1^{n} = 1 .$
$We know that i^{3} = - i .$
$Thus, 1 \cdot (- i) = - i .$
$Hence the answer is (D).$

Attempt this question & track your score

Sign up free to answer, get instant scoring, and let SolveGini track which Mathematics topics you need to revise.

Attempt & Track Free →

More Complex Numbers practice questions

View all Complex Numbers questions →