ikoreanx3
Divide. Rewrite the expression so that the imaginary unit does not appear in the denominator.
5+8i/9i



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ikoreanx3
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\[\frac{ 5+8i }{ 9i }\]

anonymous
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multiply top and bottom by \(i\)

some_someone
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\[\frac{ 5 + 8i }{ 9i }\]
\[\frac{ 5 + 8i }{ 9i }\times \frac{ 9i }{ 9i }\]
\[\frac{ 9i(5 + 8i) }{ 81 }\]

anonymous
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get
\[\frac{5i8}{9}\]

anonymous
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then you can rewrite it as
\[\frac{8}{9}\frac{5}{9}i\]

some_someone
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\[\frac{ 45i  72 }{ 81 }\]

some_someone
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\[\frac{ 8 }{ 9 }  \frac{ 5 }{ 9 }i\]