Easy -1.8 This is a simple multiple-choice question testing basic properties of complex conjugates. Students only need to check each statement (the fourth is false since z - z* = 2iΒ·Im(z) while z* - z = -2iΒ·Im(z)), requiring minimal calculation and no problem-solvingβwell below average difficulty even for Further Maths.
Given that \(z\) is a complex number, and that \(z^*\) is the complex conjugate of \(z\), which of the following statements is not always true?
Circle your answer.
[1 mark]
\((z^*)^* = z\) \quad\quad \(zz^* = |z|^2\) \quad\quad \((-z)^* = -(z^*)\) \quad\quad \(z - z^* = z^* - z\)
Given that $z$ is a complex number, and that $z^*$ is the complex conjugate of $z$, which of the following statements is \textbf{not always} true?
Circle your answer.
[1 mark]
$(z^*)^* = z$ \quad\quad $zz^* = |z|^2$ \quad\quad $(-z)^* = -(z^*)$ \quad\quad $z - z^* = z^* - z$
\hfill \mbox{\textit{AQA Further Paper 2 2019 Q1 [1]}}