Question

prove that :1+i¹⁰+i¹⁰⁰+i¹⁰⁰⁰=2​

Answer 1

Answer:

Step-by-step explanation:

since i= √-1

i²=-1

i³= -i

i⁴= 1

and this cycle repeats

so, 1+ i¹⁰+i¹⁰⁰- i¹⁰⁰⁰ = 1+ -1+1-1= 0. :)

Answer 2

We know:

${i}^{x} = { - 1}^{ \frac{x}{2} }$

Thus

$1 + {i}^{10} + {i}^{100} + {i}^{1000}$

$= 1 + { - 1}^{5} + { - 1}^{50} + { - 1}^{500}$

$= 1 + ( - 1) + 1 + 1$

$= 2$