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FP2 Transformations in the complex plane

Hi,

I am struggling to make any further progression with question 6 (a).

I have made Z the subject, taken the modulus of both sides and ended up with:

3=∣iw∣∣1−w∣ 3 = \frac{|iw|}{|1-w|}

However, I don't know what to do here. I've tried substituting w = u + iv into there, but when I square both sides to remove the moduli, it becomes a mess with lots of i terms, which I don't know how to deal with. The mark scheme says something about using Pythagoras, but I'm not entirely sure how that is relevant here? :frown:



ImageUploadedByStudent Room1421702631.180948.jpg




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TeeEm
19
Original post by kingaaran
Hi,

I am struggling to make any further progression with question 6 (a).

I have made Z the subject, taken the modulus of both sides and ended up with:

3=∣iw∣∣1−w∣ 3 = \frac{|iw|}{|1-w|}

However, I don't know what to do here. I've tried substituting w = u + iv into there, but when I square both sides to remove the moduli, it becomes a mess with lots of i terms, which I don't know how to deal with. The mark scheme says something about using Pythagoras, but I'm not entirely sure how that is relevant here? :frown:



ImageUploadedByStudent Room1421702631.180948.jpg




Posted from TSR Mobile


•

multiply across

•

use w = u + iv

•

group real and imaginary

•

use definition of modulus

•

square both sides

•

simplify

•

complete squares

•

read circle particulars

Reply 2
Avatar for crashMATHS
crashMATHS
OP
16
Original post by TeeEm

•

multiply across

•

use w = u + iv

•

group real and imaginary

•

use definition of modulus

•

square both sides

•

simplify

•

complete squares

•

read circle particulars



What do you mean by 'use definition of modulus'?


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TeeEm
19
Original post by kingaaran
What do you mean by 'use definition of modulus'?


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|a+bi|=√(a2+b2)
Reply 4
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crashMATHS
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16
Original post by TeeEm
|a+bi|=√(a2+b2)


THANK YOU SO MUCH :biggrin:


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TeeEm
19
Original post by kingaaran
THANK YOU SO MUCH :biggrin:


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my pleasure
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crashMATHS
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16
Original post by TeeEm
my pleasure



One question - how did the mark scheme get (u-1)^2 - got (1-u)^2. I'm assuming they took -1 out of the modulus, but would that make a difference to the answer?


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TeeEm
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Original post by kingaaran
One question - how did the mark scheme get (u-1)^2 - got (1-u)^2. I'm assuming they took -1 out of the modulus, but would that make a difference to the answer?


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no difference

should be obvious by expanding that (u-1)2 = (1-u)2
Reply 8
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crashMATHS
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Original post by TeeEm
no difference

should be obvious by expanding that (u-1)2 = (1-u)2


Oh yeah, I'm so silly haha! Thanks though :smile:


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TeeEm
19
Original post by kingaaran
Oh yeah, I'm so silly haha! Thanks though :smile:


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no worries

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