Question

Find the cube roots of -1.
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Answer 1

Answer:

Let x = cbrt(-1)

=> x³ = -1

=> x³ + 1 = 0

=> (x + 1)(x² - x + 1) = 0

=> x + 1 = 0 or x² - x + 1 = 0

=> x = -1

Or

$x = \frac{ - ( - 1) + - \sqrt{ {( - 1)}^{2} - 4 \times 1 \times 1 } }{2 \times 1}$

That is

$x = \frac{1 + - \sqrt{1 - 4} }{2}$

That is

$x = \frac{1 + 3i}{2} \: \: x = \frac{1 - 3i}{2}$

Hence, cuberoots of -1 are

$- 1 \: \: \: \frac{1 + 3i}{2} \: \: \: \frac{1 - 3i}{2}$

HOPE THIS HELPS...