Question

show that (-1 + √3i)^3 is real number​

Answer 1

Answer:

√3 i - 1)³

using the formula

(a - b)³ = a³ - b³ - 3 a²b + 3 ab²

expanding the cube

(√3)³ i³ - 1³ - 3 (√3 i)² (1) + 3 (√3 i) (1)²

- 3√3 i - 1 - 9 i² + 3√3 i

- 3√3 i - 1 - 9 (-1) + 3√3 i                     (Since i² = - 1)

- 3√3 i - 1 + 9 + 3√3 i

8

hence proved

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