Question

If x = (10 − 3i) and y = (3 − 10i), then xy= and x/y=

Answer 1

Xy= (10-3i)(3-10i)
=30-100i- 9i+30i^2
=30^2-109i+30

Answer 2

Answer:  $xy=-109i,$

and

$\dfrac{x}{y}\dfrac{60}{109}+\dfrac{91}{109}i.$

Step-by-step explanation:  We are given two complex numbers as follows :

$x=10-3i,~~~~~y=3-10i.$

To find $xy$ and $\dfrac{x}{y}.$

We have

$xy\\\\=(10-3i)(3-10i)\\\\=30-9i-100i+30i^2\\\\=30-109i-30\\\\=-109i,$

and

$\dfrac{x}{y}\\\\\\=\dfrac{10-3i}{3-10i}\\\\\\=\dfrac{(10-3i)(3+10i)}{(3-10i)(3+10i)}\\\\\\=\dfrac{30-9i+100i-30i^2}{9-100i^2}\\\\\\=\dfrac{30+91i+30}{9+100}\\\\\\=\dfrac{60+91i}{109}\\\\\\=\dfrac{60}{109}+\dfrac{91}{109}i.$

Thus,

$xy=-109i,$

and

$\dfrac{x}{y}=\dfrac{60}{109}+\dfrac{91}{109}i.$