What is the result of the difference (2+i)(3-2i)-(1-2i)(2-i) ?

We'll use the property of multiplication to be
distributive over addition:

(2+i)(3-2i) = 2*(3-2i) +
i*(3-2i)

(2+i)(3-2i) = 6 - 4i + 3i -
2i^2

(2+i)(3-2i) = 6 - i -
2i^2

But i^2 = -1:

(2+i)(3-2i)
= 6 - i + 2

(2+i)(3-2i) = 8 - i
(1)

We'll calculate the 2nd
product:

(1-2i)(2-i) = 1*(2-i) -
2i*(2-i)

(1-2i)(2-i) = 2 - i - 4i +
2i^2

(1-2i)(2-i) = 2 - 5i -
2

(1-2i)(2-i) = -5i (2)

We'll
subtract (2) from (1):

8 - i - (5i) = 8 - i + 5i = 8 +
4i

The result of difference is: (2+i)(3-2i) -
(1-2i)(2-i) = 8 + 4i.