If iz3+z2−z+i=0, then |z| equals
4
3
2
1
We can write the given equation as z3+1iz2−1iz+1=0 or z3−iz2+iz−i2=0⇒z2(z−i)+i(z−i)=0⇒(z2+i)(z−i)=0⇒z2=−i,z=i⇒|z|2=|−i| and |z|=|i|⇒|z|2=1 and |z|=1⇒|z|=1