Specialist2023 Exam 2 Section A · Q4CAS active1 mark

Polar form of a complex quotient

If $z = -(2a + 1) + 2ai$ , where $a$ is a non-zero real constant, then $\dfrac{4a}{1 + \overline{z}}$ is equal to

1 mark

\sqrt{2}\operatorname{cis}\left(\dfrac{\pi}{4}\right)

\sqrt{2}\operatorname{cis}\left(\dfrac{3\pi}{4}\right)

\operatorname{cis}\left(\dfrac{\pi}{4}\right)

\sqrt{2}\operatorname{cis}\left(-\dfrac{3\pi}{4}\right)

\operatorname{cis}\left(-\dfrac{\pi}{4}\right)

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