if Z is a complex no. satisfying z^4+z^3+2z^2+z+1=0, then find value of modulus of z?

Hi Vishnu Priya,

Please note, the given expression is

z⁴+z³+z²+z²+z+1 = z²(z²+z+1)+1(z²+z+1) = (z²+1)(z²+z+1)

So that is equal to 0, will mean either z² = -1 or z²+z+1=0

So either z=i or z=w,w² (w is the cube root of unity)

So in all cases |z|=1.

Hope that helps.

All the best.

Regards,

Ashwin (IIT Madras).

z⁴+z³+z²+z²+z+1 = z²(z²+z+1)+1(z²+z+1) = (z²+1)(z²+z+1)

Therefore z² = -1 or z²+z+1=0

So either z=i or z=w,w²

Hence..