Complete the following exercises by applying polynomial identities to complex numbers. factor x2 + 64. check your work. factor 16x2 + 49. check your work. find the product of (x + 9i)2. find the product of (x − 2i)2. find the product of (x + (3+5i))2. , explanations and written work apprciated

1.)

   =(x-8i)(x+8i)

x^2+8ix-8ix-64i^2

x^2-64i^2

x^2-64(-1)

x^2+64

2.)

    =(4x-7i)(4x+7i)

16x^2+28ix-28ix-49i^2

16x^2-49i^2

16x^2-49(-1)

16x^2+49

3.)

    =(x+9i)(x+9i)

x^2+9ix+9ix+81i^2

x^2+18ix+81(-1)

x^2+18ix-81

4.)

    =(x-2i)(x-2i)

x^2-2ix-2ix+4i^2

x^2-4ix+4(-1)

x^2-4ix-4

5.)

    =[x+(3+5i)]^2

(x+5i+3)^2

(x+5i+3)(x+5i+3)

x^2+5ix+3x+5ix+25i^2+15i+3x+15i+9

x^2+6x+10ix+30i+25i^2+9

x^2+6x+10ix+30i+25(-1)+9

x^2+6x+10ix+30i-25+9

x^2+6x+10ix+30i-16

Hope this helps :)

check the picture below.

a negative exponent is translated as follows:

so, we have