Answer:
1) Solving -5x+y we get: [tex]\mathbf{-8-41i}[/tex]
2) Solving -x . y we get: [tex]\mathbf{-29-53i}[/tex]
3) Solving x . 2y we get: [tex]\mathbf{58+106i}[/tex]
4) Solving 2x - 3y we get: [tex]\mathbf{-15+19i}[/tex]
Step-by-step explanation:
We are given:
[tex]x = 3 + 8i\\y = 7 - i[/tex]
We need to find:
1) -5x+y
Solving:
Simply put values of x and y and add them.
[tex]-5x+y\\=-5(3+8i)+7-i\\=-15-40i+7-i\\=-15+7-40i-i\\=-8-41i[/tex]
So, Solving -5x+y we get: [tex]\mathbf{-8-41i}[/tex]
2) -x . y
Simply put values of x and y and multiply them.
[tex]-x\:.\:y\\=-(3+8i)\:.\:(7-i)\\=-3-8i\:.\:(7-i)\\=-3(7-i)-8i(7-i)\\=-21+3i-56i+8i^2\\We\:know\:that\:i^2=-1\\=-21+3i-56i+8(-1)\\=-21+3i-56i-8\\=-21-8+3i-56i\\=-29-53i[/tex]
So, Solving -x . y we get: [tex]\mathbf{-29-53i}[/tex]
3) x . 2y
Simply put values of x and y and multiply them.
[tex]x\:.\:2y\\=(3+8i)\:.\:2(7-i)\\=2(3+8i)\:.\:(7-i)\\=2(3(7-i)+8i(7-i)\\=2(21-3i+56i-8i^2)\\We\:know\:i^2=-1\\=2(21-3i+56i-8(-1))\\=2(21-3i+56i+8)\\=2(21+8-3i+56i)\\=2(29+53i)\\=58+106i[/tex]
So, Solving x . 2y we get: [tex]\mathbf{58+106i}[/tex]
4) 2x-3y
[tex]2x-3y\\=2(3+8i)-3(7-i)\\=6+16i-21+3i\\=6-21+16i+3i\\=-15+19i[/tex]
So, Solving 2x - 3y we get: [tex]\mathbf{-15+19i}[/tex]
