Complex Roots of a Quadratic Equation
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? Jad Aoun
Date: 10/25/1999 at 17:44:23 From: Doctor Schwa Subject: Re: Complex Numbers Jad, 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/
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