Last Updated Sep 27, 2025

Multiplying Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Multiplying quickly and effectively.

Learn about The Basics for your Leaving Cert Mathematics Exam. This Revision Note includes a summary of The Basics for easy recall in your Mathematics exam

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Multiplying

To multiply complex numbers, expand brackets as usual and replace $i^2=-1$ where applicable.

Example

infoNote

Given that $z=2-3i$ and $w=2+4i$, find $z \cdot w$

$$\begin{align*} z \cdot w&=(2-3i)(2+4i) \\\\ &=4+8i-6i-12i^2 \\\\ &=4+8i-6i+12 \\\\ &= 16+2i \end{align*}$$

infoNote

Similar to real numbers, complex numbers are also commutative under multiplication :

$$uzw=u(zw)=(uz)w$$

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