Question

Divide the following complex numbers.

−
3
−
15
i
−
2
+
3
i
−2+3i
−3−15i
​

Answer 1

-1/6 - 1/6 i.

Explanation:

We multiply top and bottom of the fraction by the complement of - 3 - 15i which is - 3 + 15i.

-2 + 3i (-2 + 3i)(-3 + 15i) 6 -9i - 30i - 45 -39 - 39i

--------- = ---------------------- = ---------------------- = --------------

-3 - 15i (-3 - 15i) (-3 + 15i) 9 -225 * -1 234

= 39 ( -1 - i) / 234

= -1/6 - 1/6 i