Question

please tell me how to prove this

Answer 1

$1 + {i}^{14} + {i}^{18} + {i}^{22} \\ = 1 + {( {i}^{2}) }^{7} + {( {i}^{2})}^{9} + {( {i}^{2})}^{11} \\ = 1 + {( - 1) }^{7} + {( - 1)}^{9} + {( - 1)}^{11} \\ = 1 - 1 - 1 - 1 \\ = - 2 \: \: which \: is \: a \: real \: \: number$

Answer 2

= 1 + i^14 + i^18 + i^22
= 1 + i^4×3+2 + i^4×4+2 + i^4×5+2(i^4=1 and i^2=-1)
= 1 + i^2 + i^2 + i^2
= 1 - 1 - 1 - 1
= -2
Hence proved