Question

solve plz.....................​

Answer 1

u can use i2, i3, i4, ki value...

i2 - (-1)

i3 -(_i)

i4-(1).....

use this identity....

Answer 2

${ \bold{ \green{ \underline{ \underline{ANSWER}} : - }}}$

${ \bold{ \underline{Given} : - }} \\ \\ { \bold{ \orange{ = 1 + {i}^{2} + {i}^{4} + ........ + {i}^{2n} }}} \\ \\ { \bold{ \orange{ we \: \: know \: \: that \: → i = \sqrt{ - 1} }}} \\ \\ { \bold{ \orange{→{i}^{2} = - 1 \: \: and \: \: {i}^{4} = 1 }}} \\ \\ { \bold{ \orange{⇒ 1 - 1 + 1 - 1 + .... + {( - 1)}^{n} }}} \\ \\ { \bold{ \orange{(1) \: \: if \: \: n \: \: i s \: \: even \: \: then⇒ \: \: 1}}} \\ \\{ \bold{ \orange{(2) \: \: if \: \: n \: \: is \: \: odd \: \: then \: ⇒ \: \: 0 }}} \\ \\ { \bold{ \boxed{ \red{ \mathfrak{ \huge{Hope \: \: you \: \: like \: \: it...}}}}}}$