complex numbers equation

[yda]

Im trying to solve this equation for along time

I tries to use the formulas for power 3 but it ddint help

I think it shuld be factoring the left side but I couldnt make it

 

z^9-z'^9=9|z|^4

 

please help

[yda]

Im trying to solve this equation for along time

I tries to use the formulas for power 3 but it ddint help

I think it shuld be factoring the left side but I couldnt make it

 

z^9-z'^9=9|z|^4

 

please help

[matt grime]

What does that dash mean? (z'^9)

 

Presumably complex conjugate.

 

LHS is 2*Im(z^9) which, if z is re^(i\theta), is 2r^9sin(\theta), and that equals 9r^4.

[matt grime]

What does that dash mean? (z'^9)

 

Presumably complex conjugate.

 

LHS is 2*Im(z^9) which, if z is re^(i\theta), is 2r^9sin(\theta), and that equals 9r^4.

[yda]

I tried it in the trigonometric way :

 

2r^9[isin(9*theta)]=9|z|^4

 

but where should I go from here ?

[yda]

I tried it in the trigonometric way :

 

2r^9[isin(9*theta)]=9|z|^4

 

but where should I go from here ?

[matt grime]

yep, correction to me, the LHS isn't what I sad. Note that the LHS is purely imaginary and the RHS purely real, thus there are no solutions except the trivial one, z=0, assuming z' means conjugate.

[matt grime]

yep, correction to me, the LHS isn't what I sad. Note that the LHS is purely imaginary and the RHS purely real, thus there are no solutions except the trivial one, z=0, assuming z' means conjugate.

[yda]

You are right

thanks

[yda]

You are right

thanks

[bloodhound]

same here, altough i just plugged the equation in maple and made it solve it.

[bloodhound]

same here, altough i just plugged the equation in maple and made it solve it.