Question

013. What is the value of i -999
(A) i
(B) 0
(C) -i
(D) 1​

Answer 1

Answer:

option c is the correct option

Step-by-step explanation:

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Answer 2

Answer:

The value of i⁻⁹⁹⁹ is i.

Step-by-step explanation:

Given,

The complex number i⁻⁹⁹⁹.

To find,

The value of the complex number i⁻⁹⁹⁹.

Calculation,

We know that the value of i = √(-1)

Similarly, the value of i² = -1

And the value of i³ = i² × i = -i

i⁴ = i² × i² = -1 × -1 = 1

i⁵ = i⁴ × i = i

i⁶ = i⁵ × i = i × i = -1

So from observation, we get that:

i²ⁿ = -1 (if n is a odd number)

i²ⁿ = 1 (if n is a even number)

i⁽²ⁿ ⁺ ¹⁾ = -i (if n is a odd number)...(1)

i⁽²ⁿ ⁺ ¹⁾ = i (if n is a even number)

So, our given complex number is i⁻⁹⁹⁹ = 1/i⁹⁹⁹

Now we take the power of 'i' and equate it to (2n + 1) and see what's coming.

999 = 2n + 1

⇒ n = 499

As the value of 'n' is an odd integer.

i⁹⁹⁹ = -i [from equation (1)]

Now, 1/i⁹⁹⁹ = -1/i

                  = -i/i²

                  = i

Therefore, the value of i⁻⁹⁹⁹ is i.

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