Quick questions on Roots of complex numbers (SACE Stage 2 Specialist Mathematics)

Q: What is step 1 - polar form of the right side?

8i has modulus r = 8 and lies on the positive imaginary axis, so θ = π2: $8i = 8(cos(π)/(2) + isin(π)/(2)).$

2short 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 step 1 - polar form of the right side?

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8i

has modulus

r = 8

and lies on the positive imaginary axis, so

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

: $

8i = 8\left(\cos\frac{\pi}{2} + i\sin\frac{\pi}{2}\right).

What are not reducing arguments?

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Final arguments should usually be given as principal values in

(-\pi, \pi]

; an argument like

\frac{3\pi}{2}

may be expected as

-\frac{\pi}{2}

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