Question

show that z= (-1+√-3)³ / (2)³ is rational number​

Answer 1

Answer:

a + b)³ = (a + b)(a + b)(a + b)

In (-1+√3i)³ , a = -1 & b = i√3

(-1+√3i)³ = (-1 + i√3)(-1 + i√3)(-1 + i√3)

(-1+√3i)³ = (1 - 3 - 2i√3)(-1 + i√3)

(-1+√3i)³ = (-2 - 2i√3)(-1 + i√3)

(-1+√3i)³ = -2(1 + i√3)(-1 + i√3)

(-1+√3i)³ = -2 (-1 - 3)

(-1 + i√3)³ = -2 (-4)

(-1 + i√3)³ = 8

8=8/1

The number 8 is a rational number because it can be written as the fraction 8/1.