Question

If iz^3 + z^2 -z + i =0 then |z| is?

Answer 1

ok lets see what we have here

Answer 2

man this is not that easy ... lol :)

Answer 3

\[iz^3 + z^2 -z + i =0\]\[iz^3 -i^2 z^2 -z + i =0\]\[iz^2(z-i) -(z - i) =0\]\[(z - i)(iz^2-1) =0\]

Answer 4

For all the roots
|z|=1

Answer 5

mukushla, how did you know how to do that ?

Answer 6

and...u r correct @UnkleRhaukus can u explain this

Answer 7

the factored form shows
\[(z-i)=0\]
\(z=i\) is a solution


_____
\[|z|=|i|\]

Answer 8

the other solution\[(iz^2−1)=0\]
\[iz^2=1\]
\[z=\sqrt{\frac1{i}}=\sqrt{-i}=i\sqrt i\]

Answer 9

Same result if you take the real part, then the imaginary part of both sides of the original equation.

Answer 10

\[iz^2−1=0\]\[z^2=-i\]\[|z^2|=|z|^2=1\]\[|z|=1\]

Answer 11

lol...@mukushla there will be two soln for ur eq

Answer 12

for |z| ? what are the solutions?