First slide

Algebra of complex numbers

Question

$If Z be a complex number satisfying Z^{4} + Z^{3} + 2 Z^{2} + Z + 1 = 0, then set of all possible value of |Z| is$

Moderate

A

$\{1, 2\}$
B

$\{1\}$
C

$\{1, 2, 3\}$
D

$\{1, 2, 3, 4\}$

Solution

$\begin{array}{l} The given equation is (Z^{2} + Z + 1) (Z^{2} + 1) = 0 \\ Z^{2} + Z + 1 = 0, Z^{2} + 1 = 0 \\ \Rightarrow Z = ω, ω^{2}, i, - i w h e r e ω i s c o m p l e x c u b e r o o t o f u n i t y \\ \Rightarrow | Z | = 1 \end{array}$

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