Multiplying (Leaving Cert Mathematics): Revision Notes

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Multiplying

To multiply complex numbers, expand brackets as usual and replace i2=−1i^2=-1 where applicable.

Example

Note

Given that z=2−3iz=2-3i and w=2+4iw=2+4i, find z⋅wz \cdot w

z⋅w=(2−3i)(2+4i)=4+8i−6i−12i2=4+8i−6i+12=16+2i\begin{align*} z \cdot w&=(2-3i)(2+4i) \\\\ &=4+8i-6i-12i^2 \\\\ &=4+8i-6i+12 \\\\ &= 16+2i \end{align*}
Note

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

uzw=u(zw)=(uz)wuzw=u(zw)=(uz)w
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Explore Leaving Cert Mathematics Flashcards by Topics

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The Basics

Argand Diagrams & Modulus

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Explore Leaving Cert Mathematics Exam Questions by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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