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# FP2 Transformations in the complex plane watch

1. 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:

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?

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2. (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:

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?

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• multiply across
• use w = u + iv
• group real and imaginary
• use definition of modulus
• square both sides
• simplify
• complete squares
3. (Original post by TeeEm)
• multiply across
• use w = u + iv
• group real and imaginary
• use definition of modulus
• square both sides
• simplify
• complete squares
What do you mean by 'use definition of modulus'?

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4. (Original post by kingaaran)
What do you mean by 'use definition of modulus'?

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|a+bi|=√(a2+b2)
5. (Original post by TeeEm)
|a+bi|=√(a2+b2)
THANK YOU SO MUCH

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6. (Original post by kingaaran)
THANK YOU SO MUCH

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my pleasure
7. (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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8. (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
9. (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

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10. (Original post by kingaaran)
Oh yeah, I'm so silly haha! Thanks though

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no worries

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