Solving for |a| in a Complex Number Equation

[aviravir1]

if a is a complex number which satisfy $$ia^3+a^2-a+1=0$$

then find $$\left | a \right |$$ ?

one way is to put a=x+iy

any other short way ?

 

[aviravir1]

No coments ?

 

[hamster143]

You could try using this

http://en.wikipedia.org/wiki/Cardano_formula#General_formula_of_roots

I don't see any obvious simple way. Roots seem badly irrational.

 

[aviravir1]

ok the real question was find the maximum value of $$\left | a -3-4i\right |$$

now will that help in any way making the soln shorter...i guess not..but still will it?

 

[hamster143]

Does not look like it does

http://www.wolframalpha.com/input/?i=i*+(b+++3+++4*i)^3+(b+++3+++4*i)^2-(b+++3+++4*i)+1

Should it? If it should, double check the equations ...