Question

Number 1 and 2 please (25 points)

Answer 1

Answers:

1) $(3x+2)+(4-5x)=-2x+6$

$(3+2i)+(4-5i)=7-3i$

2) $(1-3x)(2+x)=-3x^{2}-5x+2$

$(1-3i)+(2+i)=5-5i$

Step-by-step explanation:

In mathematics there are rules related to complex numbers, specifically in the case of addition and multiplication:

Addition:

If we have two complex numbers written in their binomial form, the sum of both will be a complex number whose real part is the sum of the real parts and whose imaginary part is the sum of the imaginary parts (similarly as the sum of two binomials).

For example,  the addition of these two binomials is:

$(3x+2)+(4-5x)=3x-5x+2+4=-2x+6$

Similarly, the addition of two complex numbers is:

$(3+2i)+(4-5i)=3+4+2i-5i=7-3i$ Here the complex part is the number with the $i$

Multiplication:

If we have two complex numbers written in their binomial form, the multiplication of both will be the same as the multiplication (product) of two binomials, taking into account that $i^{2}=-1$.

For example,  the multiplication of these two binomials is:

$(1-3x)(2+x)=2+x-6x-3x^{2}=-3x^{2}-5x+2$

Similarly, the multiplication of two complex numbers is:

$(1-3i)+(2+i)=2+i-6i-3i^{2}=2-5i-3(-1)=5-5i$