Adding & Subtracting (Leaving Cert Mathematics): Revision Notes

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Adding & Subtracting

When adding complex numbers, add real components together and imaginary components together. More formally if z1=a+biz_1=a+bi and z2=c+diz_2=c+di then :

z1+z2=(a+c)+(b+d)iz_1 +z_2=(a+c)+(b+d)i

For subtraction, you need to account for the brackets :

z1−z2=(a+bi)−(c+di)=a+bi−c−di=(a−c)+(b−d)i\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+4iz=11+4i and w=9−7iw=9-7i, find z+wz+w.

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

Now find z−wz-w :

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

Explore Leaving Cert Mathematics Model Answers by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Quizzes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

Explore Leaving Cert Mathematics Flashcards by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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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