Question

If (x+iy)^3=u+iv
then show that..............................

Answer 1

\[\LARGE \frac{u}{x}+\frac{v}{y}=4(x^2-y^2)\]

Answer 2

@shubhamsrg @ParthKohli @Callisto

Answer 3

expand LHS and compare maybe ?

Answer 4

\[\LARGE x^3-y^3-3xy^2+3x^2iy=u+iv\]

Answer 5

3x^iy=iv?

Answer 6

3x^2iy=iv*?

Answer 7

Just a thought: \(N(x + yi) = x^2 + y^2\). So \(N((x + yi)^3) = (x^2 + y^2)^3\).

Also, \(N (u + vi) = u^2 + v^2\)\[(x^2 + y^2)(x^2 + y^2)(x^2 + y^2) = u^2 + v^2\]

Answer 8

I don't know if that's the method heh.

Answer 9

got it guys thanks,no not you @ParthKohli :P

Answer 10

lol

Answer 11

lol

Answer 12

\[\LARGE x^3-iy^3+3x^2iy+3x i^2y^2\]

Answer 13

Sahi hai, last two terms factor kar lo.

Answer 14

Ohhh, got it! @shubhamsrg was right... compare :-P

Answer 15

someone call @yrelhan4 :/

Answer 16

yeah compared and gotcha

Answer 17

u=x^3-3xy^2

Answer 18

(y)

Answer 19

why so many people???please

Answer 20

embarrasing

Answer 21

These questions are interesting. :-)

Answer 22

nahhh don't mind us, go on

Answer 23

log(x+iy) , in case you'd want to try that way ?

Answer 24

WHAT LOG WHY

Answer 25

just an alternative method, hmm, you may ignore it though, nvm! ^_^

Answer 26

ignored

Answer 27

yrelhan4 ka time khatam. its time to RnR :P

Answer 28

yuhuuuuuuuuuuuuu :P

Answer 29

Aur meri itni besti mat kiya kar.. :/ @shubhamsrg

Answer 30

rock n roll :P

Answer 31

ooo teri! new id! :O

Answer 32

we have a winner her e<3

Answer 33

haan.. medal vaapis le shivam :/

Answer 34

no :P

Answer 35

http://24.media.tumblr.com/b0dd51406c29d36dc45623b32cec8201/tumblr_mj7y2rACff1ra79gmo1_500.png

Answer 36

lol 2 medals

Answer 37

Hmm. Thank you! :/

Answer 38

http://i.qkme.me/35btfs.jpg

Answer 39

LAWL ! :D

Answer 40

Hmm. :/

Answer 41

Chalo bye.

Answer 42

:)