2022HSCMultiple choice

Q6

1 mark

Question

It is known that a particular complex number $z$ is NOT a real number. Which of the following could be true for this number $z$ ?

A. $\bar z=iz$

B. $\bar z=|z^2|$

C. $\operatorname{Re}(iz)=\operatorname{Im}(z)$

D. $\operatorname{Arg}(z^3)=\operatorname{Arg}(z)$

Try the question before revealing the answer.

Syllabus alignment

Complex Numbers

Arithmetic of complex numbersRepresent and calculate with complex numbers in Cartesian form, including conjugates, division, reciprocals and square roots.
Geometric representation of a complex numberRepresent complex numbers in the complex plane and use modulus, argument and polar form with their identities.

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