# FP1 Complex Numbers helpWatch

#1
Can anyone help me with question 6iii please

0
4 years ago
#2
(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
0
4 years ago
#3
(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
0
4 years ago
#4
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?
1
4 years ago
#5
(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.
0
4 years ago
#6
(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.
0
4 years ago
#7
(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
0
4 years ago
#8
(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!
0
#9
Thanks guys
0
4 years ago
#10
(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.
0
4 years ago
#11
(Original post by kkboyk)
Thanks guys
Np. Give us some rep and we'll call it even.
0
4 years ago
#12
(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.

0
4 years ago
#13
(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.

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.
1
4 years ago
#14
(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.

0
4 years ago
#15
(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.

Who is Sidis?
0
4 years ago
#16
(Original post by TeeEm)
Who is Sidis?
Check him out on Wikipedia - hardly a good advertisement for teaching methods!!
0
4 years ago
#17
(Original post by davros)
Check him out on Wikipedia - hardly a good advertisement for teaching methods!!

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 ...
0
4 years ago
#18
(Original post by TeeEm)

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!)
0
#19
(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.
0
4 years ago
#20
(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.
0
X

new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• Cardiff Metropolitan University
Sat, 27 Apr '19
• University of East Anglia
Could you inspire the next generation? Find out more about becoming a Primary teacher with UEA… Postgraduate
Sat, 27 Apr '19
• Anglia Ruskin University
Health, Education, Medicine and Social Care; Arts, Humanities and Social Sciences; Business and Law; Science and Engineering Undergraduate
Sat, 27 Apr '19

### Poll

Join the discussion

#### Have you registered to vote?

Yes! (551)
37.82%
No - but I will (114)
7.82%
No - I don't want to (102)
7%
No - I can't vote (<18, not in UK, etc) (690)
47.36%