Argand diagram transformations

<p style="text-align: center">${z={{\left( 2+3\mathbf{i} \right)}^{4n+2}}+{{\left( 3-2\mathbf{i} \right)}^{4n+2}}}$, ${n\in \mathbb{N}}$</p>
<p>Show clearly that&nbsp;${z=0}$ for all ${n\in \mathbb{N}}$.</p>

${z={{\left( 2+3\mathbf{i} \right)}^{4n+2}}+{{\left( 3-2\mathbf{i} \right)}^{4n+2}}}$, ${n\in \mathbb{N}}$

Show clearly that ${z=0}$ for all ${n\in \mathbb{N}}$.

Modulus, Argument, and Operations on Complex Numbers

Complex Numbers

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Complex Numbers - Modulus, Argument, and Operations on Complex Numbers

Complex Numbers - Modulus, Argument, and Operations on Complex Numbers

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