Question

interpret geometricly
\[|z_{1}^{2}+z_{2}^{2}|+|z_{1}^{2}-z_{2}^{2}|=2(|z_{1}^{2}|+|z_{2}^{2}|)\]

Answer 1

sry made a mistake:
\[|z_{1}+z_{2}|^{2}+|z_{1}-z_{2}|^{2}=2(|z_{1}^{2}|+|z_{2}^{2}|)\]

Answer 2

how to geometrically interpret the multiplication of complex number??

Answer 3

z1*z2 turn z1 by an angle of arg(z2) and shrink/strech by |z2|

Answer 4

but i don't see how this will help me here

Answer 5

since this are reals

Answer 6

i suppose addition of complex number is like vector addition?

Answer 7

ya

Answer 8

right

Answer 9

" z1*z2 turn z1 by an angle of arg(z2) and shrink/strech by |z2| "

isn't z1 and z2 symmetric ... i thought same could be applied to z1

Answer 10

wut?

Answer 11

z1*z2 turn z2 by an angle of arg(z1) and shrink/strech by |z1|

Answer 12

where you see any multiplication of z1*z2. There is not

Answer 13

isn't z1xz2 = z2xz1??

Answer 14

it is, but where u can use this?

Answer 15

@myko you were right ... so was my idea of symmetricity

Answer 16

let's try to interpret the LHS of your equation