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### Complex Roots of a Quadratic Equation

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Date: 10/25/1999 at 12:01:05
From: Aoun Family
Subject: Complex Numbers

Hi,

I have a question concerning complex numbers:

The roots of the quadratic equation z^2+pz+q = 0 are 1+i and 4+3i.
Find the complex numbers p and q. This was easy, the answers were:

p = -5 - 4i   and   q = 1 + 7i

Now for the second part of the question. It is given that 1+i is also
a root of the equation

z^2 + (a+2i)z + 5+ib = 0

where a and b are real. Determine the values of a and b. I am getting
a and b as complex numbers.

Can you help me?
```

```
Date: 10/25/1999 at 17:44:23
From: Doctor Schwa
Subject: Re: Complex Numbers

Very nicely done on the first problem.

For the second problem, there are certainly answers where a and b are
complex, but there is an answer where they are both real, too. If
you're assuming that (1+i) is a root, then you can plug in z = 1 + i,
and the equation should be true. Since it's a complex number equation,
the real and imaginary parts must both equal 0, so you get two
equations with two (real) unknowns, a and b.

If that hint doesn't make sense to you, please write back and I'll try
to explain it in a different way that might work better for you.

- Doctor Schwa, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Imaginary/Complex Numbers

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