Math Is Fun Forum

juantheron

Member

Registered: 2011-10-19

Posts: 312

complex no

Let a,b,c,d be real numbers. Sauppose that all the roots of the equation z^4 + az^3 + bz^2 + cz + d = 0 are complex numbers

lying on the circle |z| = 1 in the complex plane. The sum of the reciprocals of the roots is necessarily:

options;

a) a

b) b

c) -c

d) d

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: complex no

Hi juan

Do you know Viete's fornulas?

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

juantheron

Member

Registered: 2011-10-19

Posts: 312

Re: complex no

Thanks  anonimnystefy Got it

Let

be the roots of Given Equation

Now all Roots are Imaginary and lie on

and Imaginary Roots are always occur in pair

so Let

and

Similarly 

and

Now Using Vieta, s Formula

So

So

because

Last edited by juantheron (2012-04-28 15:06:06)

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: complex no

Parts of LaTeX are not showing. Please try to fix them.

You seem to have written a\lpha instead of alpha.

Last edited by anonimnystefy (2012-04-28 15:02:50)

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: complex no

Good,you have corrected the LaTeX.

And your work is correct! Good job!

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.