[Xarren]

z^2 - 2iz -2 = 0

z1 = i+1, z2 = i-1

The transformation

w=(az+b)/(z+d) where z does not equal -d and where a, b and d are complex numbers, maps the complex number z onto the complex number w. Given that z1 and z2 are invariant under this transformation and that z=0 maps to w=i,

a) find the values of a, b and d.


Total what the ****? Never seen a question of this type. I've been stuck for ages attempting this, and I haven't yet worked out a suitable method. Any ideas?

[BabyMaths]

Applying the transformation to z1, z2 and 0 will give you plenty of information.

[Xarren]

(Original post by BabyMaths)
Applying the transformation to z1, z2 and 0 will give you plenty of information.

Good point. I'll do that now Thanks. God knows why I didn't think of that.

[BabyMaths]

(Original post by Xarren)
Good point. I'll do that now Thanks. God knows why I didn't think of that.

In fact keeping it general for a while might be easier.

For the invariant points you have which gives the quadratic and you can compare this to the given quadratic.

Incidentally I think the question is inconsistent.

[Xarren]

(Original post by BabyMaths)
In fact keeping it general for a while might be easier.

For the invariant points you have which gives the quadratic and you can compare this to the given quadratic.

Incidentally I think the question is inconsistent.

Thanks, haven't even had a chance to have a look at it yet - madly burning through all the exercises in the book. Messed up my M3 exam so badly I now need 100 UMS on my FP2 to have any chance of going to uni xD.

Does this kind of stuff actually come up on the exams? Or did someone just feel like being a prick when writing the review exercises in the book?