Question

2) A expressao i25+ i60 e igual a:
a)0
b)i
c)-i
d)-2i
e)1+i

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Answer 1

Olá,

$\sf \: {i}^{25} + {i}^{60}$

Para fazer essa conta, vamos considerar que:

$\sf \: {i}^{2} = - 1$

Assim:

$\sf \: {i}^{25} + {i}^{60} \\ \sf \: = {i}^{24 + 1} + {( {i}^{2}) }^{30} \\ \sf \: = {i}^{24} . \: {i}^{1} + ( - 1 {)}^{30} \\ \sf \: = {(i {}^{2}) }^{12} . \: i + 1 \\ \sf \: ( - 1 {)}^{12} . \: i + 1 \\ \sf \: = 1. \: i + 1 \\ \sf \: = i + 1$

$\boxed{ \sf \: e)} \: \checkmark$