Show that the solutions for #1 + z^4 + z^3 + 2 z^2 =0# obey the condition #absz = 1# ?

2 Answers
MattyMatty
Dec 21, 2017

#|z| = 1#

Explanation:

#"This is a symmetric equation. Those can be solved with the"#
#"substitution t = z + 1/z : "#
#=> t^2 + t = 0.#
#=> t = 0 or t = -1#
#=> z^2 + 1 = 0 or z^2 + z + 1 = 0#
#=> z = pm i or z = (-1 pm sqrt(3) i)/2#
#=> |z| = 1#

Cesareo R.
Dec 21, 2017

#absz = 1#

Explanation:

#1 + z^4 + z^3 + 2 z^2 = (1+z^2)(1+z+z^2) = 0#

then #absz = 1#

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