complex numbers prob (1 Viewer)

[king.rafa]

if p is real and -2<p<2 show that the roots of the equation x^2+px+1=0 are non real complex numbers with modulus 1

hey can anyone help me prove the modulus 1 part

thanks

 

[ssglain]

As a hint, think about the relationship between the two roots and an expression that involves them and their moduli.

The full solution is attached.

 

[kony]

because p is real, the roots are in conjugate pairs.

now conjugate pairs have the same moduli.

you also know that for roots R1 and R2, R1R2 = 1.

|R1R2| = 1
now |R1|=|R2|

therefore, |R1| = 1

hence, the roots of P(x)=0 have the same moduli 1.