FP1 Complex Numbers help Watch

kkboyk
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Can anyone help me with question 6iii please

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davros
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(Original post by kkboyk)
Can anyone help me with question 6iii please

What have you tried?

If you know the 2 roots you can work this out by brute force, but I think there's a neater way of doing it too
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Doctor_Einstein
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(Original post by kkboyk)
Can anyone help me with question 6iii please

(i)

To show, just substitute it in to give:

LHS = (2+i)^2 - 4(2+i) + 5 = 4 + 4i +i^2 - 8 - 4i + 5

And since i^2 = -1, we have,

LHS = 4 + 4i -1 - 8 - 4i + 5 = 0
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aznkid66
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You know what Im(z) and Re(z) is, right?
Isn't it just simple arithmetic, then? Show what progress you've made. Did you get Im(z1^2+z2^2)=0?
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Doctor_Einstein
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(Original post by kkboyk)
Can anyone help me with question 6iii please

(i)

cont.

Since 2+i is a root, by the complex conjugate root theorem, the complex conjugate is also a root, that is 2 - i.
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Doctor_Einstein
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(Original post by kkboyk)
Can anyone help me with question 6iii please

6iii:

z1^2 + z2^2 = (2+i)^2+(2-i)^2 = 4 +4i -1 + 4 - 4i -1 = 6

Im(6) = 0 [ That is there is no imaginary component].

Therefore Im(z1^2 + z2^2) = 0.
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Doctor_Einstein
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(Original post by kkboyk)
Can anyone help me with question 6iii please

For the second part of 6(iii):

Use the fact that a^2 - b^2 = (a+b)(a-b),

So, z1^2 - z2^2 = (z1 + z2)(z1 - z2) = 4*2i = 8i.

Therefore Re(z1^2 - z2^2) = 0
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davros
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(Original post by Doctor_Einstein)
6iii:

z1^2 + z2^2 = (2+i)^2+(2-i)^2 = 4 +4i -1 + 4 - 4i -1 = 6

Im(6) = 0 [ That is there is no imaginary component].

Therefore Im(z1^2 + z2^2) = 0.

(Original post by Doctor_Einstein)
For the second part of 6(iii):

Use the fact that a^2 - b^2 = (a+b)(a-b),

So, z1^2 - z2^2 = (z1 + z2)(z1 - z2) = 4*2i = 8i.

Therefore Re(z1^2 - z2^2) = 0
Are you aware about the rule about not giving full solutions in this forum?

You haven't even given the OP a chance to do any work on this!
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kkboyk
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Thanks guys
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Doctor_Einstein
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(Original post by davros)
Are you aware about the rule about not giving full solutions in this forum?

You haven't even given the OP a chance to do any work on this!
Mate the best way to learn is to see a worked solution. William James Sidis became the smartest person in the world because he was taught by direct instruction, the most efficient learning method.

The OP had no clue and he is now smarter having seen my approach.
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Doctor_Einstein
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(Original post by kkboyk)
Thanks guys
Np. Give us some rep and we'll call it even.
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davros
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(Original post by Doctor_Einstein)
Mate the best way to learn is to see a worked solution. William James Sidis became the smartest person in the world because he was taught by direct instruction, the most efficient learning method.

The OP had no clue and he is now smarter having seen my approach.
1) Please don't call me "mate" - I am not your mate

2) You could have provided a worked solution using different numbers to illustrate the method,

3) We don't know that the OP "had no clue" - he could probably have got there with a bit of prompting but we'll never know now because you barged in and posted full solutions.

I'll let it go this time, but if you disregard the forum rules again I'll report it to the mods.

Please stick to hints and advice in future
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Doctor_Einstein
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(Original post by davros)
1) Please don't call me "mate" - I am not your mate

2) You could have provided a worked solution using different numbers to illustrate the method,

3) We don't know that the OP "had no clue" - he could probably have got there with a bit of prompting but we'll never know now because you barged in and posted full solutions.

I'll let it go this time, but if you disregard the forum rules again I'll report it to the mods.

Please stick to hints and advice in future
Mate, whether the OP could have gotten there with prompting isn't the point. The point is that it is more efficient to teach directly, than to allow a student to "get there by prompting". Sidis is the perfect example and it would be a shame for his legacy to go to waste.
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davros
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(Original post by Doctor_Einstein)
Mate, whether the OP could have gotten there with prompting isn't the point. The point is that it is more efficient to teach directly, than to allow a student to "get there by prompting". Sidis is the perfect example and it would be a shame for his legacy to go to waste.
No, the point is that there are rules for posting in this forum and you seem incapable of respecting or observing them.

Your comments about Sidis are inane and irrelevant.
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TeeEm
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(Original post by davros)
No, the point is that there are rules for posting in this forum and you seem incapable of respecting or observing them.

Your comments about Sidis are inane and irrelevant.
Who is Sidis?
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davros
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(Original post by TeeEm)
Who is Sidis?
Check him out on Wikipedia - hardly a good advertisement for teaching methods!!
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TeeEm
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(Original post by davros)
Check him out on Wikipedia - hardly a good advertisement for teaching methods!!
I read the whole thread ...

Maybe you should put your age on public display and you will not be addressed as "mate" by teenagers asking for reps! (see post 11 / I am still laughing).

If it makes you feel any better I am routinely addressed by teenagers in real life (not on line) directly by my surname like a teacher would address a pupil in the old grammar schools.

no "sir", no "Dr .....", , no "Mr ....."

I resigned to the fact I cannot change the world ...
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davros
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(Original post by TeeEm)
I read the whole thread ...

Maybe you should put your age on public display and you will not be addressed as "mate" by teenagers asking for reps! (see post 11 / I am still laughing).

If it makes you feel any better I am routinely addressed by teenagers in real life (not on line) directly by my surname like a teacher would address a pupil in the old grammar schools.

no "sir", no "Dr .....", , no "Mr ....."

I resigned to the fact I cannot change the world ...
It's not relevant to the Maths forum, but I do wonder whether some of these kids who routinely address complete strangers on the internet as "mate", "bro" or "man" are going to do this when they turn up for job interviews or have to talk to colleagues or customers as part of their jobs (assuming they get one!)
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kkboyk
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(Original post by davros)
It's not relevant to the Maths forum, but I do wonder whether some of these kids who routinely address complete strangers on the internet as "mate", "bro" or "man" are going to do this when they turn up for job interviews or have to talk to colleagues or customers as part of their jobs (assuming they get one!)
You can't really assume that, since this is supposed to be a site for students and no-one isn't really that stupid to do it in a job interview.
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Mr M
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(Original post by Doctor_Einstein)
Mate the best way to learn is to see a worked solution. William James Sidis became the smartest person in the world because he was taught by direct instruction, the most efficient learning method.

The OP had no clue and he is now smarter having seen my approach.
Now that you have finished congratulating yourself I'll sure you'll make a greater effort to comply with the Forum Rules in the future.
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