Question

Complex numbers help

Answer 1

\[\LARGE If(1+i)(1+2i)(1+3i)...(1+n i)=a+ib\]
Then..2x5x10x...(1+n^2)=?

Answer 2

@hartnn @yrelhan4 @shubhamsrg @ParthKohli

Answer 3

\[(1^2 + 1^2)(1^2 + 2^2)(1^2 + 3^2)\cdots(1 + n^2)\]Now because \(a^2 + b^2 = (a + bi)(a - bi)\), we have\[(1 + i)(1 - i)(1 + 2i)(1 - 2i)(1 + 3i)(1 - 3i)\cdots(1 + ni)(1 - ni)\]Because we have the thing you gave above,\[= (a + bi)\times (1 - i)(1 -2i)(1 - 3i)\cdots(1 - ni)\]

Answer 4

Wow, maine Shivam ka question answer kar diya :')

Answer 5

Hey, I wonder if \((1 -i)(1 - 2i)(1 - 3i)\cdots (1 - ni)\) simplifies to \(a - bi\). :-\

Answer 6

What is the final answer is the?

Answer 7

Oh yeah, it does simplify to \(a - bi\) lol.

The final answer \((a + bi)(a - bi) = a^2 + b^2\)

Answer 8

I didn't understand a word you wrote :P
What are you trying to say?

Answer 9

Hmm, dekho... \(2 \times 5 \times 10 \cdots (1 + n^2) = (1^2 + 1^2) \times (1^2 + 2^2)\times (1^2 + 3^2)\cdots (1^2 + n^2) \).

Aur ek identity hai \(x^2 + y^2 = (x + yi)(x - yi)\). Usko har bracket ki factoring ke liye use karo.

Answer 10

Jaise ki \(1^2 + 1^2 = (1 + 1i)(1 - 1i)\) aur \(1^2 + 2^2 = (1 + 2i)(1 - 2i)\)

Answer 11

oh :O

Answer 12

Toh aapke paas ye result aaya.\[(a + bi)\times\color{#C00}{(1 -i)(1 - 2i)(1 - 3i)\cdots(1 - ni)} = (a +bi)\color{#C00}{(a - bi)} = a^2 + b^2 \]

Answer 13

Is my answer correct? :|

Answer 14

yeah ..................................

Answer 15

OK. ^_^

Answer 16

i didn't get the last step you wrote o.o

Answer 17

\[(1^2 + 1^2) \times (1^2 + 2^2 ) \cdots (1^2 + n^2) = (1 + i)(1 - i) \times (1 + 2i)(1 - 2i) \cdots \times (1 + ni)(1 - ni)\]Yahan tak clear hai?

Answer 18

(Y)

Answer 19

Oh bete ki, yeh toh screen ke bahar hi bhag gaya.

Ab jin complex numbers mein beech mein ek PLUS SIGN hai, unko saath mein le aao, aur jin complex numbers mein beech mein MINUS SIGN hai, unko alag saath mein le aao.\[(1 + i)(1 + 2i)(1 + 3i)\cdots (1 + ni) \times (1 - i)(1 - 2i)(1 - 3i)\cdots (1 - ni)\]

Answer 20

\[\color{#C00}{(1 + i)(1 + 2i)(1 + 3i)\cdots (1 + ni)} \times \color{blue}{(1 - i)(1 - 2i)(1 - 3i)\cdots (1 - ni)}\]Red wala toh aapke question mein diya hua hai, aur blue wala uska conjugate hai.

Answer 21

Sab theek? ^_^

Answer 22

(Y)

Answer 23

Toh aaya \(\color{#C00}{(a + bi)}\color{blue}{(a - bi)}\).

Use \((x + yi)(x - yi) = x^2 + y^2\). :-D

Answer 24

<3

Answer 25

\[\Huge \color{red}{\heartsuit ♥ \heartsuit ♥ \heartsuit }\]

Answer 26

hmm latex :P

Answer 27

:-)

Answer 28

simply both side mod lena tha! ^_^

Answer 29

:D

Answer 30

Mera answer galat hai? T_T

Answer 31

bilkul sahi hai, kabhi galat hua hai ans? ^_^

Answer 32

@TPK

Answer 33

lolol, aapka method easy hai

Answer 34

These are wayyyy tooooo advanced for me /-\

Answer 35

@Callisto I smell liars! ^_^

Answer 36

@shubhamsrg tum karke batao O.o ek step ka answer?

Answer 37

#benedict cumberbatch

Answer 38

#HashtagsDontWorkOnOS
#NowShowHowToGetTheAnswerWithYourMethodPleaseEXCLAMATIONMARK

Answer 39

just take the modulus of both sides

Answer 40

Right side ka toh \(\sqrt{a^2 + b^2}\) hai. Left side ka...?

Answer 41

show us plz

Answer 42

I don't know how to work with absolute values of complex numbers. I've just started with them :-\

Answer 43

please kya kya hai, abhi kar deta hu! :')

Answer 44

sqrt(1^2 + 1^2) sqrt(1^2 + 2^2) .....sqrt(1^2 +n^2) = sqrt(a^2 +b^2)

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Answer 45

:'-)
OMG

Answer 46

<3>

Answer 47

yaar @yrelhan4 nahi aya, medal kise dun? :P

Answer 48

I'd have used that if I ever knew \(|(a + bi )(x + yi)| = |a + bi| \times |x + yi|\).

DLS ko de do ^_^

Answer 49

lol

Answer 50

http://i0.kym-cdn.com/entries/icons/original/000/007/423/untitle.JPG

Answer 51

Achcha phil apne paash lakh lo! ^_^

Answer 52

Dee ell ech, aap apna medal Choobhum ko de do! ^_^

Answer 53

You've already chosen the best response.

Answer 54

mai to bas @yrelhan4 ko hi dunga! B|

Answer 55

Mela le lo, phil Choobhum ko de do! ^_^

Answer 56

merko smaj nahi aya usne kya bolatoNO

Answer 57

"Undo"

Answer 58

nvm, I gave the medal! ;)

Answer 59

lol

Answer 60

Nice resolution.

Answer 61

@DLS Next question poocho!

Answer 62

English please? /-\

Answer 63

Oh. :-(

Answer 64

I see what do did there @DLS ;)

Answer 65

@shubhamsrg arre @ParthKohli ek step wala method batao na

Answer 66

you*

Answer 67

He has already written that method... @DLS

Answer 68

-_-

Answer 69

ok

Answer 70

SBS

Answer 71

Aapki DP mein aapki aankh laal ho gayi hai. Lagta hai aankh ka operation karwana hoga aapko. Lagta hai isliye hi nahi dekh paaye :-)

Answer 72

someone give me the medal too imm th eodd one here

Answer 73

@Callisto