The roots of are
.
If then that means is imaginary. So we can say , where is some multiple of .
So
.
So the two roots are complex conjugates.
The question:
Use the properties of the complex conjugate to show that if the complex number 'z' is a root of a quadratic equation with a, b, c being real coefficients, then so is the conjugate of 'z'.
My attempt:
Let z =
Basically, I changed the quadratic formula to look like a complex number in Cartesian form. Is this an acceptable answer? My textbook doesn't have solutions for 'show' and 'prove' questions.
Thanks!
Hello, Glitch!
I have a very primitive solution . . .
Use the properties of the complex conjugate to show that
if the complex number is a root of a quadratic equation
with real coefficients,
then so is the conjugate of
We are told that is a solution of the quadratic.
. . Hence: .
This simplifies to: .
. . And we have: .
The conjugate of is: .
Consider
. . . . . . .