If `i z^3+z^2-z+i=0` , where `i=sqrt(-1)` , then `|z|` is equal to 1 (b) `1/2` (c) `1/4` (d) None of these

Explanation

we have
`iz^(3) =z^(2) -z +i=0`
`Rightarrow i(z) (z^(2)+i) + (z^(2)+i)=0`
` Rightarrow (z^(2) +i)(iz+1)=0`
` Rightarrow " Either " z^(2)+ i =0 or iz+ 1 =0`
`" when " z^(2) +i=0`
` Rightarrow z^(2)=-i`
`Rightarrow |z^(2)|=|-i|=1`
`Rightarrow |z|=1 , as |z|` can't be negative .
when iz+1 =0
` Rightarrow z = -1/i = i`
` Rightarrow |z| = |i| =1 `
in either case , |z| =1 .