Last Updated Sep 27, 2025

Adding & Subtracting Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Adding & Subtracting 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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Adding & Subtracting

When adding complex numbers, add real components together and imaginary components together. More formally if $z_1=a+bi$ and $z_2=c+di$ then :

$$z_1 +z_2=(a+c)+(b+d)i$$

For subtraction, you need to account for the brackets :

$$\begin{align*} z_1-z_2&=(a+bi)-(c+di)\\ &=a+bi-c-di \\ &= (a-c)+(b-d)i \end{align*}$$

Example

infoNote

Given that $z=11+4i$ and $w=9-7i$, find $z+w$.

$$\begin{align*} z+w&=(11+4i)+(9-7i) \\\\ &=(11+9)+(4-7)i \\\\ &=20-3i \end{align*}$$

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Now find $z-w$ :

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$$\begin{align*} z-w&=(11+4i)-(9-7i) \\\\ &=11+4i-9+7i \\\\ &=(11-9)+(4i+7i) \\\\ &= 2+11i \end{align*}$$

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