More help I need lots of help mostly mentally but this too

Explanation:

If we multiply some complex number a+bi with its conjugate a-bi, then we get the real number a^2+b^2. You can use the FOIL rule to confirm that (a+bi)(a-bi) = a^2+b^2 is true. Recall that i = sqrt(-1), so i^2 = -1.

In this case, a = 4 and b = 5, so,

(a+bi)(a-bi) = a^2+b^2

(4+5i)(4-5i) = 4^2+5^2

(4+5i)(4-5i) = 41

We see that x = 4 and y = -5 must be the case.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.