Complex Numbers Quadratics

Question

1. The complex number 3 - 4i is one root of the quadratic equation x^2 + bx + c = 0.

a) Which of the choices is the second root of this equation?

1) -3 + 4i
2) 3 + 4i
3) 3 - 4i
4) -3 - 4i

b) Find the values of b and c

c) simplify: square root of (-3+4i)(3+4i)

d)8i/16 = x/4i

Find the product of all five answers and 2i^3.

I'm on a site called Mathbits, and to be able to get to the next page of questions, I need every single answer to be correct and then do the last operation listed (the product of all five answers, etc)

The answers I have are

1a) #2

b)0 and 25

2)5i

3)x = -2

Need help before tomorrow (2/6/17), Thanks!

Answer 1

All the answers are correct except for the second one, the correct answer to it is b =-6 and c=25. As you already have two roots from question 1, you can get equation by (x-a)(x-b)=0 where a and b are root of quadratic equation.

So, (x-3+4i)(x-3-4i)=0 will give you required equation

After solving this, you can compare it with the given equation and you will get b=-6 and c=25

Answer 2

Another way you could do it is say $x=3-4i\to x-3=-4i\to (x-3)^2=-16\to \boxed{x^2-6x+25=0}$