How do you divide #3/(5i)#?

2 Answers
MathFact-orials.blogspot.com
Sep 18, 2016

#3/(5i)=(3i^4)/(5i)=(3i^3)/5=-3/5i#

Explanation:

Keep in mind that #i=sqrt(-1)# which means that #i^2=-1# and therefore #i^4=1#. So we can rewrite the question as:

#(3i^4)/(5i)=(3i^3)/5#

#i^3=-sqrt(-1)=-i# and so:

#(3i^4)/(5i)=(3i^3)/5=-3/5i#

Jim G.
Sep 18, 2016

#-3/5i#

Explanation:

To divide this fraction we require the denominator to be a real number.

This is achieved in this case by multiplying the numerator/denominator by i.

#rArr3/(5i)=3/(5i)xxi/i=(3i)/(5i^2)#

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(i^2=(sqrt(-1))^2=-1)color(white)(a/a)|)))#

#rArr(3i)/(5i^2)=(3i)/(-5)=-3/5i#

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