What is the principal square root of a negative number?

The principal square root of a negative number is expressed in terms of 'i', the imaginary unit.

What is the relationship between real numbers and imaginary numbers?

Real numbers are on the number line, while imaginary numbers are perpendicular to the real number line in the complex plane.

What is a complex number?

A complex number is a number that can be expressed in the form $$a + bi$$ , where a and b are real numbers.

How do you add two complex numbers?

To add two complex numbers, add their real parts and their imaginary parts separately.

How do you multiply two complex numbers?

To multiply two complex numbers, use the distributive property and apply the fact that $$i^2 = -1$$ .

What is the modulus of a complex number $$a + bi$$ ?

The modulus is given by $$|a + bi| = \sqrt{a^2 + b^2}$$ .

Imaginary numbers Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is an imaginary number?

Back

An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as $i = \frac{\text{sqrt}(-1)}{1}$ .

2.

FLASHCARD QUESTION

Front

What is the value of $i^2$ ?

Back

$i^2 = -1$ .

3.

FLASHCARD QUESTION

Front

Simplify $2 \sqrt[]{-45}$ .

Back

$6i \sqrt[]{5}$ .

4.

FLASHCARD QUESTION

Front

Simplify $\sqrt[]{-25}$ .

Back

$5i$ .

5.

FLASHCARD QUESTION

Front

What is the solution to the equation $-3x^2 + 8 = 12$ ?

Back

$\pm \frac{2i\sqrt{3}}{3}$ .

6.

FLASHCARD QUESTION

Front

Simplify $\sqrt[]{-4}$ .

Back

$2i$ .

7.

FLASHCARD QUESTION

Front

Solve for x: $5x^2 + 5 = -600$ .

Back

$\pm 11i$ .

9.

FLASHCARD QUESTION

Front

How do you express $\sqrt[]{-a}$ in terms of 'i'?

Back

$\sqrt[]{-a} = i\sqrt{a}$ for any positive real number a.

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