Question

find value of i⁹⁹⁹ .​

Answer 1

Answer:

No matter what the power of 1 is,the answer will be 1. So 1^999=1.

Answer 2

Answer:

i⁹⁹⁹ = -i

Step-by-step explanation:

Concept used:

• i² = -1
• i³ = (i × i × i) = (i² × i) = (-1 × i) = -i
• i⁴ = (i²)² = (-1)² = 1

→ So, we can conclude that when i is raised to the power of even number divisible by 4, we get the answer as 1.

→ Else, if i is raised to a power containing an even number that is not divisible by 4 then the answer would be -1

→ Also, when i is raised to an odd number (as in here) then just split the power using laws of exponents.

Solution:

i⁹⁹⁹ can also be written as i⁹⁹⁸ × i¹ by applying laws of exponents.

998 is an even number and is not divisible by 4.

So, the value of i⁹⁹⁸ = -1.

Hence,

$\sf{i^{999}=(i^{998}\times i)=(-1 \times i) = -i}$

$\therefore \boxed{\bf{i^{999}=-i}}$