Question

the value of i5+i6+i7+i8 is​

Answer 1

The value of $i^5+i^6+i^7+i^8$ is equal to "zero (0)".

Step-by-step explanation:

We have:

$i^5+i^6+i^7+i^8$

To find, the value of $i^5+i^6+i^7+i^8$ = ?

∴ $i^5+i^6+i^7+i^8$

= $i^5+i^5(i)+i^5.i^2+i^5(i^3)$

Taking $i^{5}$ as common, we get

= $i^5(1+i+i^2+i^3)$

Using the complex number identity,

$i^{2} = -1$

= $i^5(1+i-1+i^2(i))$

= $i^5(1+i-1-i)$

= $i^5(0)$

= 0

∴ The value of $i^5+i^6+i^7+i^8$ = 0

Thus, the value of $i^5+i^6+i^7+i^8$ is equal to "zero (0)".

Answer 2

$\large { \fcolorbox{gray}{black}{ ✔\: \textbf{Verified \: answer}}}$

The value of i⁵ + i⁶ + i⁷ + i⁸ is equal to 0 (zero).