Question 1
Given \(z \in \mathbb{C}\), where \(z \neq 0\), prove \(|z^2| = |z|^2\).
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Specialist Mathematics Β· Unit 3 Β· Further complex numbers Β· Complex arithmetic using polar form
Prove complex number identities involving modulus and argument, e.g. π§ π§Μ = |π§|2, |π§1| |π§2| = |π§1 π§2| and arg(π§1 π§2) = arg(π§1) + arg(π§2).
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Question 2
A complex number \(z = x + yi\), where \(x, y \in \mathbb{R}\) and \(z \neq 0\), is shown on the Argand diagram. Prove that \(|z^2| = |z|^2\).
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