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  4. If (a+i b)5=α+i β then (b+i a)5 is equal to

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Q. If $(a+i b)^5=\alpha+i \beta$ then $(b+i a)^5$ is equal to

Complex Numbers and Quadratic Equations

Solution:

$(a+i b)^5=\alpha+i \beta$
$i^5(b-i a)^5=\alpha+i \beta$
$(b-i a)^5=-i \alpha+\beta$
$(b+i a)^5=\beta+i \alpha$