If z is a non - real root of -1- then z 86- z 175- z 289 is equal to-A- -1B- 0C- 1D- 3

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Euler's Representation

If z is a non...

Question

If z is a non - real root of $\sqrt[7]{- 1}$ , then $z^{86} + z^{175} + z^{289}$ is equal to:

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Solution

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z

\sqrt[7]{- 1}

z^{86} + z^{175} + z^{289}

3 \times 3

P \neq Q .

P^{3} = Q^{3} a n d P^{2} Q = Q^{2} P,

(P^{2} + Q^{2})

Question 13

In the following question, out of the four options, only one is correct. Write the correct answer:

If y be any non-zero integer, then $y^{0}$ is equal to:
(a) 1
(b) 0
(c) -1
(d) Not defined

∣ ∣ ∣ ∣ \begin{matrix} x & - 6 & - 1 2 & - 3 x & x - 3 - 3 & 2 x & x + 2 \end{matrix} ∣ ∣ ∣ ∣ = 0,

$Δ P Q R$ is right angled at Q. S is the mid-point of QR and $P R^{2} = a (P S)^{2} + b (P Q)^{2}$

Then a + b is equal to:

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