Quick questions on De Moivre's theorem and roots of complex numbers: VCE Specialist Mathematics Unit 3

Q: What is not reducing to the principal argument?

Arguments like (7π)/(6) should be brought into (-π, π] by adding or subtracting 2π when a principal value is asked for.

Q: What is q1?

Use De Moivre's theorem to evaluate (1 + i)^6. [3 marks]

Q: What is q2?

Find all solutions of z^4 = 16. [3 marks]

Q: What is q3?

A real cubic has roots -1 and 1 + 2i. State its third root and a real quadratic factor. [2 marks]

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is not reducing to the principal argument?

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Arguments like

\frac{7\pi}{6}

should be brought into

(-\pi, \pi]

by adding or subtracting

2\pi

when a principal value is asked for.

What is q1?

Show answer

Use De Moivre's theorem to evaluate

(1 + i)^6

. [3 marks]

What is q2?

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Find all solutions of

z^4 = 16

. [3 marks]

What is q3?

Show answer

A real cubic has roots

-1

and

1 + 2i

. State its third root and a real quadratic factor. [2 marks]

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