The Modulus (Leaving Cert Mathematics): Quizzes

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The Modulus
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What does the modulus of a complex number measure?

Distance from origin on Argand diagram

What is the formula for the modulus of z=a+biz = a + bi?

∣z∣=a2+b2|z| = \sqrt{a^2 + b^2}

What type of number is the modulus of a complex number?

A positive real number or zero

Which mathematical theorem is the modulus formula based on?

Pythagoras' theorem

How is the modulus of a complex number zz written in notation?

∣z∣|z|

What is ∣3+4i∣|3 + 4i|?

55

What is ∣−2+3i∣|-2 + 3i|?

13\sqrt{13}

In the Argand diagram, what does the modulus represent geometrically?

The hypotenuse of a right triangle

What does the triangle inequality state for complex numbers z1z_1 and z2z_2?

∣z1∣+∣z2∣≥∣z1+z2∣|z_1| + |z_2| \geq |z_1 + z_2|

To find ∣z1+z2∣|z_1 + z_2|, what should you do first?

Add the complex numbers, then find modulus

Explore Leaving Cert Mathematics Revision Notes by Topics

Fundamentals of Complex Numbers

The Basics

Argand Diagrams & Modulus

Solving Equations

DeMoivre's Theorem

Transformations

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 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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