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# Fp1

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1. A complex number z is given by z=(1+2i)^2 +((3+i)/(1+i))
Express z in the form x+iy?
Ive expanded the (1+2i)^2 to get 4i-3 , when i times the other function by the conjugate to have to times it by 4i +3 too?
2. No.
3. No
4. Okay thanks guys , ill work it out & ill tell you what i got in a minute
5. I got 3i+5 , is that right? Its a 2001 paper , so couldnt fine the mark scheme
6. (Original post by Ayaz789)
I got 3i+5 , is that right? Its a 2001 paper , so couldnt fine the mark scheme
No you should get .You should've got , then you multiply top and bottom of to get and add those together.
7. (Original post by IrrationalRoot)
No you should get .You should've got , then you multiply top and bottom of
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\frac{3+i){1+i}
to get and add those together.
Its not showing it properly , the message you wrote:/
8. (Original post by Ayaz789)
Its not showing it properly , the message you wrote:/
Fixed, Latex is being stupid for some reason.
9. (Original post by IrrationalRoot)
No you should get .You should've got , then you multiply top and bottom of to get and add those together.
Ahh i made a silly mistake at the end , instead of taking away from 2 i added 3 to 2 to get 5:/
10. (Original post by IrrationalRoot)
Fixed, Latex is being stupid for some reason.
Top man!
11. (Original post by IrrationalRoot)
Fixed, Latex is being stupid for some reason.
So is the modulus Root 10?
And the argument is tan-1(3/-1) which is -1.25
Do i do Pi minus that answer to get 1.89?
12. (Original post by Ayaz789)
So is the modulus Root 10?
And the argument is tan-1(3/-1) which is -1.25
Do i do Pi minus that answer to get 1.89?
Correct modulus.
for argument.
13. (Original post by IrrationalRoot)
Correct modulus.
for argument.
Whats arctan3?
14. (Original post by Ayaz789)
Whats arctan3?
Same as i.e. the angle the position vector of the complex number makes with the negative real axis, so you do minus that to get the argument which is the angle it makes with the positive real axis.
15. (Original post by IrrationalRoot)
Same as i.e. the angle the position vector of the complex number makes with the negative real axis, so you do minus that to get the argument which is the angle it makes with the positive real axis.
Is my argument right of 1.89?
16. (Original post by Ayaz789)
Is my argument right of 1.89?
Yes, but I hope you understand the method and how it works.
17. (Original post by IrrationalRoot)
Yes, but I hope you understand the method and how it works.
Can you repeat why its not tan (3/-1)
18. (Original post by Ayaz789)
Can you repeat why its not tan (3/-1)
It's not because that will give you a fourth quadrant angle, and you know the complex number is in the second quadrant. You would need to add to to get the argument.

Alternatively, do what I do and draw a little sketch of the right triangle on an Argand diagram.
19. (Original post by IrrationalRoot)
It's not because that will give you a fourth quadrant angle, and you know the complex number is in the second quadrant. You would need to add to to get the argument.

Alternatively, do what I do and draw a little sketch of the right triangle on an Argand diagram.
Ahh okay just the -1 is confusing me thats all!:/
20. (Original post by Ayaz789)
Ahh okay just the -1 is confusing me thats all!:/

If you draw this sort of diagram it becomes clear. The red angle you find using trigonometry, and then the green angle is your argument which you find by doing pi-red angle.

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