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Complex number 4+5(-1/2 +i square root 3/2)^334 +3(-1/2 +i square root 3/2 )^365 is equal to

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Solution: Using $-1/2 +isqrt3/2=omega$ , We can write the

given expression as,

$Rightarrow$ $4+5omega ^334+3omega ^365=4+5omega +3omega ^2=1+2omega =sqrt3i$ .

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Deependra Verma

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