The three roots 3 + i, -3 + i and -2i all have modulus 2 and are spaced 120^ apart, as required.

QLDSpecialist MathematicsQuick questions

Unit 3: Mathematical induction, and further vectors, matrices and complex numbers

Quick questions on Complex numbers in polar form and de Moivre's theorem (QCE Specialist Mathematics Unit 3)

Q: What is roots of a complex number?

To solve w^n = z where z = re^iθ, the n distinct roots are

Q: What is convert to polar form?

Here z = 8i lies on the positive imaginary axis, so r = 8 and θ = π2. Thus z = 8\,e^iπ/2.

3short 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 roots of a complex number?

Show answer

To solve

w^n = z

where

z = re^{i\theta}

, the

n

distinct roots are

What is convert to polar form?

Show answer

Here

z = 8i

lies on the positive imaginary axis, so

r = 8

and

\theta = \dfrac{\pi}{2}

. Thus

z = 8\,e^{i\pi/2}

What is check?

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The three roots

\sqrt3 + i

-\sqrt3 + i

and

-2i

all have modulus

2

and are spaced

120^\circ

apart, as required.

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