Question

B)
(x + iy) (3 + i) = 2 + 4i​

Answer 1

`x = 1`

`y=1`

Step-by-step explanation:

Given

`(x + iy)(3 + i) = 2 + 4i`

Required

Find x and y

Open brackets

`3x + x.i + 3y. i + y.i.i = 2 +4i`

`i.i = -1`

So:

`3x + x.i + 3y. i - y = 2 +4i`

Rewrite as:

`3x - y+ x.i + 3y. i = 2 +4i`

By comparison:

`3x - y = 2` --- (1)

`x + 3y = 4` --- (2)

Make x the subject in
`x + 3y = 4`

`x = 4-3y`

Substitute
`x = 4-3y` in
`3x - y = 2`

`3(4 - 3y)- y=2`

`12 - 9y- y=2`

`12 - 10y=2`

Collect like terms

`-10y = 2- 12`

`-10y = - 10`

`y=1`

Substitute
`y=1` in
`x = 4-3y`

`x = 4 - 3 * 1`

`x = 4 - 3`

`x = 1`