Thread: Factorisation

This isn't urgent, but I'd like explanations + working out so I can understand the question. THanks!

Factorise:

2z^2 + 2(z-2)z +3/2 - 6i

Originally Posted by phgao

This isn't urgent, but I'd like explanations + working out so I can understand the question. THanks!

Factorise:

2z^2 + 2(z-2)z +3/2 - 6i

This is a complex quadratic, so you can proceed by completing the square,
or using the quadratic formula to find its roots and then the
factorisation is:

.

So lets simplify the equation a bit:



The only problem will be finding the square root of the discriminant.
In this case the discriminant is:



We need the square root of this. We proceed by converting the discriminant
to polar form, then finding the square root by square-rooting the modulus and
halving the argument. Or as MathWorld would put it:

,

Which should allow you to complete the factorisation.

RonL