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Quadratic Equations

The equation ...

Question

The equation $z^{5} + z^{4} + z^{3} + z^{2} + z + 1 = 0$ is satisfied by

z = \pm 1

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z = - 1

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\pm \frac{1}{2} + i \frac{\sqrt{3}}{2}

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\frac{1}{2} \pm i \frac{\sqrt{3}}{2}

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Solution

The correct options are
B $z = - 1$
D $\frac{1}{2} \pm i \frac{\sqrt{3}}{2}$

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Similar questions

z_{1}, z_{2}, z_{3}, z_{4}, z_{5}

z^{5} + z^{4} + z^{3} + z^{2} + z + 1 = 0

∣ ∣ ∣ ∣ 5 \sum i = 1 z_{i}^{4} ∣ ∣ ∣ ∣

z^{5} + z^{4} + z^{3} + z^{2} + z + 1 = 0

i z^{2}

1 + \frac{2}{z} + \frac{3}{z^{2}} + \frac{4}{z^{3}} + \frac{5}{z^{4}} + . . . .

z = n \pm \sqrt{- i}

⌊ 100 n ⌋

z_{1}, z_{2}, z_{3}

z_{4}

z^{4} + z^{3} + z^{2} + z + 1 = 0

\begin{matrix} Column I & Column II (A) & ∣ ∣ ∣ ∣ 4 \sum i = 1 (z_{i})^{4} ∣ ∣ ∣ ∣ is equal to & (p) & 0 (B) & 4 \sum i = 1 (z_{i})^{5} is equal to & (q) & 4 (C) & 4 \prod i = 1 (z_{i} + 2) is equal to & (r) & 1 (D) & Least value of [| z_{1} + z_{2} |] is & (s) & 11 \end{matrix}

where []

z^{5} + z^{4} + z^{3} + z^{2} + z + 1 = 0

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