Definition (Leaving Cert Mathematics): Quizzes

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Who assumed a solution exists for x2=−1x^2 = -1 and named it ii?

Euler

What is the imaginary unit ii defined as?

i=−1i = \sqrt{-1}

Which equation has no solution in real numbers, leading to imaginary numbers?

x2=−1x^2 = -1

What is the general form of an imaginary number?

aiai

What is the general form of a complex number?

a+bia + bi

What is i2i^2 equal to?

−1-1

What is i3i^3 equal to?

−i-i

What is i4i^4 equal to?

11

What is the repeating pattern for powers of ii?

i,−1,−i,1i, -1, -i, 1

In the standard form a+bia + bi, what condition makes a complex number real?

b=0b = 0

In the form a+bia + bi, what condition makes a complex number purely imaginary?

a=0a = 0

What is −16\sqrt{-16} equal to?

4i4i

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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