Question

: If iz3 + z2 - Z + i = 0, then show that | z | = 1.​

Answer 1

Answer:

Z= x+iy

Z³= (x+iy)³= x³+3ix²y-3xy²-iy³

Z²=(x+iy)²= x²+2ixy-y²

iZ³+ Z²- Z + i = 0

or, x³i -3x²y-3ixy²+y³+x²+2ixy-y²-x-iy+i=0

or, i(x³-3xy²+2xy-y+1) +(y³-3x²y+x²-y²-x) =0

so, x³-3xy²+2xy-y+1 =0

&

y³-3x²y+x²-y²-x=0

solving these two equation we get,

x=0 & y=1

so, |Z| = 1