Maths HL Complex Numbers questions

Troxck

I'll get to the point, I have no idea how to do the following questions, I've attempted them all and have gotten the wrong answer consistently. I'm not really sure what to do and my Maths teacher isn't someone who is happy with you just attempting them a few times and getting the wrong answer, they must be right and that's that. So if you could help in anyway, that would be great!

The questions are questions 14-16 and are on Page 320 of Active Maths 4 Book 1.

Moody_mona

This is the conjugate root theorem. This theorem states that if a quadratic has real coefficients, and z is a root, then so is z bar - the conjugate of z. Remember the conjugate is when you change the sign of the imaginary part, so if z = a + bi then z conjugate or z bar is a - bi.

This question also links back to algebra, where every quadratic is written as x^2 - (sum of the roots)x +(product of the roots).

I don't want to give you the answers straight out, does any of that help?

Troxck

Moody_mona wrote: »

This is the conjugate root theorem. This theorem states that if a quadratic has real coefficients, and z is a root, then so is z bar - the conjugate of z. Remember the conjugate is when you change the sign of the imaginary part, so if z = a + bi then z conjugate or z bar is a - bi.

This question also links back to algebra, where every quadratic is written as x^2 - (sum of the roots)x +(product of the roots).

I don't want to give you the answers straight out, does any of that help?

I understand the CRT and how z bar is also a root if z is a root.

I understand that every quadratic is also written as x^2.

Although this has helped greatly I am still confused in regards to question 16.

Moody_mona

OK, so put that quadratic in the form x^2...... Which means you'll have to divide across by b2. Then try equating the coefficient of X to - (sum of the roots) and the constant on its own to the product of the roots.

For the second part, you might need to divide the real root in first.