Question

The value of i-999 is ( i power -999)​

Answer 1

SOLUTION

TO DETERMINE

The value of

$\sf {i}^{ - 999}$

EVALUATION

We know that i is the complex number satisfying the property

$\sf {i}^{ 2} = - 1$

Now we have

$\sf {i}^{ - 999}$

$\sf = { \big( {i}^{2} \big) }^{ - 499} . {i}^{ - 1}$

$\displaystyle \sf = { \big( - 1 \big) }^{ - 499} . \frac{1}{i}$

$\displaystyle \sf = - \frac{1}{i}$

$\displaystyle \sf = - \frac{i}{ {i}^{2} }$

$\displaystyle \sf = - \frac{i}{ - 1}$

$\displaystyle \sf = i$

FINAL ANSWER

$\sf {i}^{ - 999} = i$

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Answer 2

Answer:

i=√-1

i²= -1

i⁴= 1

so 999/4=249 and remainder is 3

so we can write

(i⁴)²⁴⁹* i³

i⁴=1 and i³= -i

so,

(1)²⁴⁹* -i

=1* -i

= -i