Question

${i}^{4} + 2 {i}^{6} - 3 {i}^{8} + 7 {i}^{10}$

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Answer 1

Hello Mate,

Here is your answer,

We Know that,

${i}^{2} = - 1$

Then,

${i}^{4}</p><p> \\ \\ = { ({i}^{2}) }^{2} \\ \\ = { - 1}^{2} \\ \\ = 1$

${i}^{6} </p><p> \\ \\ { ({i}^{2}) }^{3} \\ \\ = { - 1}^{3} \\ \\ = - 1$

${i}^{8} </p><p> \\ \\ = { ({i}^{2}) }^{4} \\ \\ { - 1}^{4} \\ \\ = 1$

${i}^{10}</p><p> \\ \\ = { ({i}^{2}) }^{5} \\ \\ = { - 1}^{5} \\ \\ = - 1$

Now substitute all the values, we get,

${i}^{4} + 2 {i}^{6} - 3 {i}^{8} + 7 {i}^{10} \\ \\ = 1 + 2( - 1) - 3(1) + 7( - 1) \\ \\ = 1 - 2 - 3 - 7 \\ \\ = - 11$

Hence the answer is - 11

Hope it helps:)

Answer 2

$\large\underline{ \underline{ \sf \: Answer : \: \: }}$

$\star \: \: \sf - 11$

$\large\underline{ \underline{ \sf \: Solution : \: \: }}$

$\sf \implies {(i)}^{4} + 2 {(i)}^{6} - 3 {(i)}^{8} + 7 {(i)}^{10} \\ \\ \sf \implies { ({i}^{2}) }^{2} + 2{( {i}^{2} )}^{3} - 3 {( {i}^{2} )}^{4} + 7 { ({i}^{2}) }^{5} \\ \\\sf \implies { (- 1)}^{2} + 2 {( - 1)}^{3} - 3 {( - 1)}^{4} + 7 {( - 1)}^{5} \\ \\\sf \implies 1 + 2( - 1) - 3(1) + 7( - 1) \\ \\\sf \implies 1 - 2 - 3 - 7 \\ \\\sf \implies - 1 - 10 \\ \\ \sf \implies - 11$

Hence , the final answer is - 11

$\large\underline{ \underline{ \sf \: Remmember : \: \: }}$

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