Last updated on Oct 23, 2026

Quadratic Equations With Complex Roots (Leaving Cert Mathematics): Quizzes

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Quadratic Equations With Complex Roots

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When does a quadratic equation have complex roots?

When $b^2 - 4ac < 0$

What is the expression $b^2 - 4ac$ called?

The discriminant

If $2 + 3i$ is a root, what is the other root?

$2 - 3i$

In the standard form $a + bi$ , what does $i$ represent?

$\sqrt{-1}$

What variable is typically used for quadratics with complex roots?

$z$

What is the value of $i^2$ ?

$-1$

For $z^2 + 6z + 10 = 0$ , what is the discriminant?

$-4$

What is $\sqrt{-4}$ simplified?

$2i$

What are the roots of $z^2 + 4z + 5 = 0$ ?

$-2 \pm i$

If $-3 + i$ is a root, what is its conjugate pair?

$-3 - i$

What is $(3 + i)^2$ expanded?

$8 + 6i$

If $z = 3 + i$ is a root of $z^2 - 6z + k = 0$ , find $k$ .

$10$

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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