Easy -1.8 This is a straightforward recall question requiring only knowledge that e^(iπ) = -1, so e^(i·2π) = 1, making z^6 = e^(i·2π) = 1 real. It's a 1-mark multiple choice question with minimal calculation, significantly easier than average A-level questions which typically require multi-step problem-solving.
The complex number \(z = e^{\frac{i\pi}{3}}\)
Which one of the following is a real number?
Circle your answer.
[1 mark]
\(z^4\) \(z^5\) \(z^6\) \(z^7\)
The complex number $z = e^{\frac{i\pi}{3}}$
Which one of the following is a real number?
Circle your answer.
[1 mark]
$z^4$ $z^5$ $z^6$ $z^7$
\hfill \mbox{\textit{AQA Further Paper 1 2024 Q2 [1]}}