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

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### 1 Answer

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.**