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FP2 Complex Numbers Transformations

There's no answer for this question, so i was wondering if someone could check if i've got the right answer because i improvised and wasn't sure if i just made up some method rules along the way :confused:

Question:

Transformation: w = (4-z)/(z+i)
The circle |z|=1 is transformed by this onto a line.


I ended up with U = 1.5, anyone else?
Reply 1
Avatar for Notnek
Notnek
21
Original post by minnigayuen
There's no answer for this question, so i was wondering if someone could check if i've got the right answer because i improvised and wasn't sure if i just made up some method rules along the way :confused:

Question:

Transformation: w = (4-z)/(z+i)
The circle |z|=1 is transformed by this onto a line.


I ended up with U = 1.5, anyone else?

You haven't posted the whole question.
Reply 2
Avatar for the bear
the bear
20
did they want the equation of the line ?
Reply 3
Avatar for BabyMaths
BabyMaths
Original post by minnigayuen

Transformation: w = (4-z)/(z+i)
The circle |z|=1 is transformed by this onto a line.


I ended up with U = 1.5, anyone else?


I have 2u−8v=152u-8v=15
Reply 4
Avatar for BabyMaths
BabyMaths
If on the other hand you meant w=4−zz+1\displaystyle w=\frac{4-z}{z+1} then the line is u=1.5.
Original post by BabyMaths
If on the other hand you meant w=4−zz+1\displaystyle w=\frac{4-z}{z+1} then the line is u=1.5.


What level is this

Can u explain your method please
Reply 6
Avatar for Notnek
Notnek
21
Original post by Yung_ramanujan
What level is this

Can u explain your method please

A Level further maths

Method: Make z the subject, set up an equation using the info in the question, sub w=u+iv, expand the moduli.
Original post by notnek
A Level further maths

Method: Make z the subject, set up an equation using the info in the question, sub w=u+iv, expand the moduli.


Oh ok. Would this come under geometry of complex numbers?
Reply 8
Avatar for Notnek
Notnek
21
Original post by Yung_ramanujan
Oh ok. Would this come under geometry of complex numbers?

Probably. I'm used to this topic being called "Transformations of the complex plane" in further maths.
Original post by notnek
Probably. I'm used to this topic being called "Transformations of the complex plane" in further maths.


What exam board is that for. Ive not come across this in my fp2
Reply 10
Avatar for BabyMaths
BabyMaths
Original post by Yung_ramanujan
What exam board is that for. Ive not come across this in my fp2



It might be Edexcel FP3.
Original post by BabyMaths
It might be Edexcel FP3.


We dont have complex numbers in our fp3!

Maybe its just not covered on ours, becayse we only have fp2&3 and our fp2 covers same topixs as others fp2-4. Any resources for me to learn this from
Reply 12
Avatar for BabyMaths
BabyMaths
Original post by Yung_ramanujan
We dont have complex numbers in our fp3!

Maybe its just not covered on ours, becayse we only have fp2&3 and our fp2 covers same topixs as others fp2-4. Any resources for me to learn this from


Actually I think it's FP2 now, on Edexcel.

As for resources to learn from you could Google it or get some cheap old textbooks.

Resources to get practice: http://www.edexcel.com/i-am-a/student/Pages/Past_papers_app.aspx

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