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Algebra of Complex Numbers

If a+i b5=α+i...

Question

If $(a + i b)^{5} = α + i β t h e n (b + i a)^{5}$
is equal to

A

β - iα

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B

β + iα

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C

α+β

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D

-α-iβ

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Solution

The correct option is B β + iα

Solution: $(a + i b)^{5} = α + i β$
Taking complex conjugate
$(a - i b)^{5} = α - i β$
$(- i^{2} a - i b)^{5} = α - i β$
$(- i)^{5} (b + a i)^{5} = α - i β$
$(b + a i)^{5} = - \frac{α}{i} + β$
$= α i + β$

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(a + i b)^{5} = α + i β

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