If iZ3+ Z2 - Z + i = 0 ' then show that mode of Z = 1 - Maths - Complex Numbers and Quadratic Equations

Question

If iZ3+ Z2 - Z + i = 0 ' then show that
mode of Z = 1

ramandeep.singh · Accepted Answer

$i z^{3} + z^{2} - z + i = 0 \Rightarrow z^{2} (i z + 1) + i (i z + 1) = 0 \Rightarrow (z^{2} + i) (i z + 1) = 0 ∴ z^{2} + i = 0 o r i z + 1 = 0 \Rightarrow z^{2} = - i o r z = \frac{- 1}{i} = i$

Thus, z = i

$∴ | z | = \sqrt{1} = 1$

Hence, proved.