Using the rules of multiplication of complex numbers, what is the result (5+2i)(2-i)?

We'll explain the multiplication of complex numbers
written in algebraic form, choosing 2 comeplx numbers:

z1 =
5+2i and z2 = 2-i

The real part of z1 = Re(z1) =
5

The imaginary part of z1 = Im(z1) =
2

The real part of z2 = Re(z2) =
2

The imaginary part of z2 = Im(z2) =
-1

We'll multiply the numbers z1*z2 =
(5+2i)(2-i)

We'll apply
FOIL:

z1*z2=10-5i+4i-2i^2

i^2
= -1

The result of (5+2i)(2-i) is z1*z2 = 12
- i