Complex NumbersHard
Question
If z is a complex number then the equation z2 + z |z| + |z2| = 0 is satisfied by
(ω and ω2 are imaginary cube roots of unity)
(ω and ω2 are imaginary cube roots of unity)
Options
A.z = k ω where k ∈ R
B.z = k ω2 where k is non negative real
C.z = k ω where k is positive real
D.z = k ω2 where k ∈ R
Solution
z = reiθ
r2eiθ2 + r2eiθ + r2 = 0
r2 [ei2θ + eiθ + 1] = 0
θ =
z = kω or where kω2 > 0
r2eiθ2 + r2eiθ + r2 = 0
r2 [ei2θ + eiθ + 1] = 0
θ =
z = kω or where kω2 > 0
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