Question

Complete the following exercises by applying polynomial identities to complex numbers. Show your work. Factor x^2 + 64. Check your work. Factor 16x^2 + 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.

Answer 1

Explanation:

Hello,

Factor x^2 + 64.

`\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}`

Factor 16x^2 + 49.

`\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}`

Find the product of (x + 9i)^2.

`\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}`

Find the product of (x − 2i)^2.

`\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}`

Find the product of (x + (3+5i))^2.

`\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you