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Knowledge Check Quiz

EXAMS.IE

De Moivre's Theorem

Hint

This is a cubic equation equation.

1 / 5

How many solutions are there to \(x^3=8\)?

Hint

\((-2)^3=-8\)

2 / 5

\(-2\) is a solution to \(x^3=8\).

Hint

No other solutions can be found by inspection.

3 / 5

How many of the solutions to \(x^3=8\) are purely real?

Hint

Purely real numbers are also complex.

4 / 5

How many of the solutions to \(x^3=8\) are complex?

Hint

The answer can be determined by using the Conjugate Roots theorem.

5 / 5

If \(x=a+bi\) is a solution to \(x^3=8\), which of the following must also be a solution?

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