Question

NEED HELP PLEASE!

Complete the following exercises by applying polynomial identities to complex numbers. Show your work.
1. Find the product of (x + (3+5i))2

Answer 1

`(x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16`

Explanation:

Complex numbers identity:

The complex numbers identity is:

`i^2 = -1`

Square of the sum:

`(x + y)^2 = x^2 + 2xy + y^2`

In this question:

`(x + (3+5i))^2`

`x^2 + 2x(3+5i) + (3+5i)^2`

`x^2 + 6x + 10xi + 9 + 30i + 25i^2`

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

`x^2 + 6x + (10x+30)i - 16`

So

`(x + (3+5i))^2 = x^2 + 6x + (10x+30)i - 16`