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

`(x)/(y)(60)/(109)+(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
`(x)/(y).`

We have

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

and

`(x)/(y)\\\\\\=(10-3i)/(3-10i)\\\\\\=((10-3i)(3+10i))/((3-10i)(3+10i))\\\\\\=(30-9i+100i-30i^2)/(9-100i^2)\\\\\\=(30+91i+30)/(9+100)\\\\\\=(60+91i)/(109)\\\\\\=(60)/(109)+(91)/(109)i.`

Thus,

`xy=-109i,`

and

`(x)/(y)=(60)/(109)+(91)/(109)i.`