Consider the following question. #10; #10; (1+i)^4+(1 i)^4= #10; #10;Using Formula, #10; #10; a^4+b^4=( #10;(a^2+b^2)^2 2a^2b^2) #10; ...

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Binomial Expression

Solve 1+i4+...

Question

Solve $(1 + i)^{4} + (1 - i)^{4} =$

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Solution

Consider the following question.

${(1 + i)}^{4} + {(1 - i)}^{4} =$

Using Formula,

$a^{4} + b^{4} = ({(a^{2} + b^{2})}^{2} - 2 a^{2} b^{2})$

${(1 + i)}^{4} + {(1 - i)}^{4} = ({(1 + i)}^{2} + {(1 - i)}^{2} - 2 (1 - i^{2}))$

$= (1 + i^{2} + 2 i + 1 + i^{2} - 2 i - 2 + 2 i^{2})$

$= - 2$

Hence, this is the required answer.

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Similar questions

{(\frac{1 + i}{1 - i})}^{4} + {(\frac{1 - i}{1 + i})}^{4} =

{(1 + i)}^{4} {(1 + \frac{1}{i})}^{4} = 16

{(1 + i)}^{4} \times {(1 + \frac{1}{i})}^{4} = 16

(1 + i)^{4} + (1 - i)^{4}

(1 + i)^{4} + (1 - i)^{4}

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