(-2+5i) (3+i) explain process of equation please

We'll recall what is the rectangular form of a complex
number, since we have to perform a multiplication of two complex
numbers:

z = a + b*i

a - the
real part of the complex number

b - the imaginary
part

i = sqrt(-1)

We'll have
to remove he brackets using FOIL method:

(-2+5i)*(3+i) =
-2*3 - 2*i + 5i*3 + 5i*i

(-2+5i)*(3+i) = -6 - 2i + 15i +
5i^2

From the complex number theory, we'll find out that
i^2 = -1, therefore, the expression will
become:

(-2+5i)*(3+i) = -6 - 2i + 15i -
5

We'll combine real parts and imaginary
parts:

(-2+5i)*(3+i) = -11 +
13i

a = the real part=-11

b =
the imaginary part = 13

The result of
multiplication of the given complex numbers is also a complex number: z = -11 +
13i.