How do you divide #4/(-3-6i)#?

1 Answer
Aug 30, 2016

Answer:

#-4/15+8/15i#

Explanation:

To divide this fraction we require the denominator to be #color(blue)"real"#

To obtain this multiply (-3 - 6i) by it's #color(blue)"conjugate"#

The conjugate of (-3 - 6i) is (-3 + 6i). Note that the real part remains unchanged while the #color(red)"sign"# of the imaginary part is reversed.

#rArr(-3-6i)(-3+6i)=9-18i+18i-36i^2=45" 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 also have to multiply the numerator by (-3 + 6i)

#4/(-3-6i)xx(-3+6i)/(-3+6i)=(4(-3+6i))/((-3-6i)(-3+6i))#

#=(-12+24i)/45=-12/45+24/45i=-4/15+8/15i#