First slide

Algebra of complex numbers

Question

If z₁ and z₂ are the complex roots of the equation $(x - 3)^{3} + 1 = 0$ , then z₁ + z₂ equal to

Moderate

A

1
B

3
C

5
D

7

Solution

$\begin{array}{l} (x - 3)^{3} + 1 = 0 \\ \Rightarrow {(\frac{x - 3}{- 1})}^{3} = 1 \\ \Rightarrow \frac{x - 3}{- 1} = 1, ω, ω^{2} \\ \Rightarrow x = 2, 3 - ω, 3 - ω^{2} \end{array}$
Hence, the sum of complex roots is $6 - (ω + ω^{2}) = 6 + 1 = 7$ .

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