Question

Divide: (5 + 4i) / (-3 – 2i)

Answer 1

-23/13 - 2/13i

Explanation:

`(5+4i)/(-3-2i)\\\\\mathrm{Apply\:complex\:arithmetic\:rule}:\\\\\quad (a+bi)/(c+di)\:=\:(\left(c-di\right)\left(a+bi\right))/(\left(c-di\right)\left(c+di\right))\:=\:(\left(ac+bd\right)+\left(bc-ad\right)i)/(c^2+d^2)\\\\a=5,\:b=4,\:c=-3,\:d=-2\\\\=(\left(5\left(-3\right)+4\left(-2\right)\right)+\left(4\left(-3\right)-5\left(-2\right)\right)i)/(\left(-3\right)^2+\left(-2\right)^2)\\\\Refine\\=(-23-2i)/(13)\\\\`

`\mathrm{Rewrite\:}(-23-2i)/(13)\mathrm{\:in\:standard\:complex\:form:\:}-(23)/(13)-(2)/(13)i\\`