How do you divide #1/(-8-5i)#?

1 Answer
Sep 8, 2016

Answer:

#-8/89+5/89i#

Explanation:

To divide this fraction we require to make the denominator real.

This can be achieved by multiplying (-8 - 5i) by it's #color(blue)"conjugate"#

If #z=x±yi# then the conjugate is.

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(barz=x∓yi)color(white)(a/a)|)))#
Note that x, remains unchanged while the sign of the imaginary part is reversed.

#rArr(-8+5i)" is the conjugate of" -8-5i#

and #(-8-5i)(-8+5i)=64-25i^2=64+25=89#

That is we have a real value on the denominator.

Since this is a fraction, we must of course multiply both numerator and denominator by the conjugate.

#rArr(-8+5i)/((-8-5i)(-8+5i))=(-8+5i)/89=-8/89+5/89i#