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# FP1 Complex numbers watch

1. It is given that 3 - i is a root of the quadratic equation z^2 -(a+bi)z +4(1+3i) =0 where a and b are real.
In either order,

a) find the values of a and b
b)find the other root of the quadratic equation, given that it is of the form ki, where k is real.

Explain why the roots do not form a conjugate pair.

I honestly don't have a clue where to start.

Any help is appreciated
2. (Original post by Super199)
It is given that 3 - i is a root of the quadratic equation z^2 -(a+bi)z +4(1+3i) =0 where a and b are real.
In either order,

a) find the values of a and b
b)find the other root of the quadratic equation, given that it is of the form ki, where k is real.

Explain why the roots do not form a conjugate pair.

I honestly don't have a clue where to start.

Any help is appreciated
Substitute in z = 3 - i and since it is a root, equate the complex expression you get to 0 and form simultaneous equations in a and b.
3. (Original post by 16Characters....)
Substitute in z = 3 - i and since it is a root, equate the complex expression you get to 0 and form simultaneous equations in a and b.
Right I have done part a now thanks . Any help with part b?
4. (Original post by Super199)
Right I have done part a now thanks . Any help with part b?
You know one root, you know the form of the second root is ki. EDIT: Use the sum of roots of x^2 + bx + c = 0 is -b if you are going to use properties of roots.

If not just divide through by a factor like in C1 for cubics.
5. (Original post by Super199)
Right I have done part a now thanks . Any help with part b?
As an alternative to the above suggestions, just put z = ki into the quadratic to get an equation for k (since you now know what a and b are).

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