Last Updated Sep 27, 2025

Dividing Simplified Revision Notes for Leaving Cert Mathematics

Revision notes with simplified explanations to understand Dividing 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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Dividing

To divide complex numbers, we eliminate the imaginary part from the denominator by multiplying the numerator and denominator by the conjugate of the denominator.

Example

infoNote

Simplify the following :

$$\frac{1+i}{2+i}$$

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First, derive the conjugate of the denominator, $\overline{2+i}=2-i$.

$$\begin{align*} \frac{1+i}{2+i}&=\frac{1+i}{2+i}\cdot \frac{2-i}{2-i} \\\\ &= \frac{2-i+2i-i^2}{4-2i+2i-i^2} \\\\ &=\frac{2-i+2i-(-1)}{4-2i+2i-(-1)} \\\\ &=\frac{3+i}{5} \end{align*}$$

Write in the form $a+bi$ :

$$\begin{align*} \frac{3+i}{5}&=\frac{3}{5}+\frac{1}{5}i \end{align*}$$

infoNote

In all cases, multiplying a complex number $z$ with it's conjugate $\overline{z}$ will eliminate the imaginary component.

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