Can we get this on the exam?

[tony3272]

Hey guys, I found this question a few days ago which is (i guess) relevant to our course, but i've never seen one like that before.
I ended up getting it, but it was incredibly tedious, so i'm wondering; Do you think VCAA can ask us something like this on the exam?

Can't remember where i saw it, but it was pretty much worded like this:

If , express in the form: and find the value of a.
Hence, show that

[Natters]

holy shit thats way too hard for me
i like that there are only 2 kinds of mathematician quote btw

[acinod]

There is a quicker way you can do that question.

You know that Re(z)=0.5(z+conjugate z) -> you can derive this since the sum of any complex number and its conjugate is twice the Real part.

So you just sub z and its conjugate into the equation above and simplify the fraction. Eventually you will get a term that is the product of z and its conjugate. Now remember the product of any complex number with its conjugate is equal to the magnitude squared so in this case it would be 1. So you sub 1 in and eventually the numerator of your fraction will equal to 0. So everything becomes 0 and you have shown what was required. (I seriously need to learn Latex...)

And also I know it said hence but this is a lot faster if you're good with conjugates and I don't think they penalise you if you don't follow the world 'hence' since you DID use what you've learnt from the course to answer the question and it's mathematically correct.

P.S. Dr He loves this question.

[99.96]

^^^^i lost you at the simplifying the fraction part to get z x its conjugate.
how exactly do you simplify it?
(z+conjugate z -2)/(z+conjugate z +2)