Answer:
[tex]x = 1[/tex]
[tex]y=1[/tex]
Explanation:
Given
[tex](x + iy)(3 + i) = 2 + 4i[/tex]
Required
Find x and y
Open brackets
[tex]3x + x.i + 3y. i + y.i.i = 2 +4i[/tex]
[tex]i.i = -1[/tex]
So:
[tex]3x + x.i + 3y. i - y = 2 +4i[/tex]
Rewrite as:
[tex]3x - y+ x.i + 3y. i = 2 +4i[/tex]
By comparison:
[tex]3x - y = 2[/tex] --- (1)
[tex]x + 3y = 4[/tex] --- (2)
Make x the subject in [tex]x + 3y = 4[/tex]
[tex]x = 4-3y[/tex]
Substitute [tex]x = 4-3y[/tex] in [tex]3x - y = 2[/tex]
[tex]3(4 - 3y)- y=2[/tex]
[tex]12 - 9y- y=2[/tex]
[tex]12 - 10y=2[/tex]
Collect like terms
[tex]-10y = 2- 12[/tex]
[tex]-10y = - 10[/tex]
[tex]y=1[/tex]
Substitute [tex]y=1[/tex] in [tex]x = 4-3y[/tex]
[tex]x = 4 - 3 * 1[/tex]
[tex]x = 4 - 3[/tex]
[tex]x = 1[/tex]
