How do you divide #(4+i)/(8i)#?

1 Answer
Sep 11, 2016

Answer:

#1/8-1/2i#

Explanation:

To divide this fraction we require the denominator to be a #color(blue)"real number " #and not a #color(blue)"complex number"# as it is.

To achieve this multiply the numerator and denominator . in this case by i.

Since: #8ixxi=8i^2=-8larr" a real number"#

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

Since this is a fraction, we must also multiply the numerator by i.

#rArr(i(4+i))/(8i^2)=(4i-1)/(-8)#

divide each term on the numerator by - 8

#rArr(4i)/(-8)-1/(-8)=1/8-1/2i" in standard form"#