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Show that if iz^3+z^2-z+i=0, then |z|=1...

Show that if `iz^3+z^2-z+i=0`, then `|z|=1`

Text Solution

Verified by Experts

Given `iz^3 +z^2 -z +I =0`
`rArr iz^3-i^2 z^2-z+i=0 [ because i^2 =-1]`
`rArr iz^2 (z-i)-1(z-i)=0`
`(iz^2-1)(z-i)=0 `
`rArr z-I =0 or iz^2-I =0`
`z=i or z^2 = 1/i =-i`
If z=i then |z| =i|=1
If `z^2=-I, then |z^2|=| -i| =1`
`rArr |z|^2 =1 rArr |z| =1`
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