Question

i^999-i^-999 pls tell me step by step How will the answer came​

Answer 1

Answer:

$- 2i$

Step-by-step explanation:

Concept

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

${i}^{4} = {( {i}^{2}) }^{2} = {( - 1)}^{2} = 1$

${i}^{4n} = {1}^{n} = 1$

Calculation

${i}^{999} - {i}^{ - 999}$

$= {i}^{999} - \frac{1}{ {i}^{999} }$

$= {i}^{4 \times 249 + 3} - \frac{1}{{i}^{4 \times 249 + 3}}$

$= {( {i}^{4}) }^{249} . {i}^{3} - \frac{1}{{( {i}^{4}) }^{249} . {i}^{3} }$

$= {1}^{249 } .{i}^{2}.i - \frac{1}{{1}^{249 } .{i}^{2}.i}$

$= 1( - 1)i - \frac{1}{1( - 1)i}$

$= - i + \frac{1}{i}$

$= - i + \frac{i}{ {i}^{2} }$

$= - i + \frac{i}{ - 1}$

$= - i - i$

$= - 2i$

Answer 2

Answer:

-2i is the answer ..........