How do I do this algebra 2 problem?

Question

How do you rationalize the denominator on this problem?
-9-9i OVER -1-8i

Also, this problem ask to Find all the real and complex zeros of the polynomial; x^4 + 4x^3 +x^2 -16x -20.

I look all over my math book but it does not teach you how to do these kind of problems. Thanks.

Answer 1

You rationalize the denominator by multiplying numerator and denominator by the complex conjugate.

The complex conjugate of (a + bi) is (a - bi).

To the problem. First multiply thru by -1, then pull out a 9 in the numerator.

(-9 - 9i)/(-1 - 8i) = (9 + 9i)/(1 + 8i) = 9(1 + i)/(1 + 8i)

Now multiply the numerator and denominator by the complex conjugate.

9(1 + i)(1 - 8i)/{(1 + 8i)(1 - 8i)}
= 9(1 - 8i + i + 8)/{(1² - (8i)²}
= 9(9 - 7i)/(1 + 64) = 9(9 - 7i)/65
___________________________

Find all the real and complex zeros of the polynomial:
x^4 + 4x^3 + x^2 - 16x - 20.

x^4 + 4x^3 + x^2 - 16x - 20
= (x - 2)(x + 2)(x² + 4x + 5)
= (x - 2)(x + 2)(x +[2 + i])(x +[2 - i])

The roots of the polynomial are:

x = -2, 2, -2+i, -2-i

Answer 2

Okay for the first problem you simply multiply the numerator and denominator by
-1+8i so that you get

(-9-9i)(-1+8i) / (-1-8i)(-1+8i)

just multiply that out and whaa laa.

For the second problem I think they want you to factor by grouping but I'm not entirely sure.

Answer 3

the area between 2 factors is predicated on the pythagorean theorem. You calculate the finished upward thrust (distinction between the y coordinates) and the run (distinction between the x coordinates), and then build a top triangle such that the hypotenuse is the line between the two factors. -14 - (-2) = -12 (your "upward thrust") 12 - 9 = 3 (your "run") by applying pyth thm, (-12)^2 + 3^2 = d^2, the place d is the area between the two factors. (-12)^2 + 3^2 = d^2 a hundred and forty four + 9 = d^2 153 = d^2 d = sqrt(153), or the sq. root of 153 = approximately 12.369. desire it helps.

Answer 4

dunno ...lol