Exploring the Complex Number System

Why is there no real number solution to the equation x² = -1?

• Because squaring any real number always results in a positive value.

• Because squaring any real number always results in a negative value.

• Because x cannot be a real number.

• Because the equation is undefined.

What is the imaginary unit 'i' defined as?

• The square root of 0

• The cube root of -1

• The square root of -1

• The square root of 1

In the complex number 3 + 4i, what is the real part?

• 7

• i

• 4

• 3

Which of the following is NOT a natural number?

• -3

• 0

• 2

• 1

What distinguishes whole numbers from natural numbers?

• Whole numbers include decimals.

• Whole numbers include negative numbers.

• Whole numbers include fractions.

• Whole numbers include zero.

Which of the following is a rational number?

• π (pi)

• √2

• e

• 0.75

What is a characteristic of irrational numbers?

• Their decimal representation terminates.

• Their decimal representation neither terminates nor repeats.

• Their decimal representation repeats.

• They can be written as fractions.

What is the simplified form of √(-7)?

• i7

• √7

• 7i

• i√7

How can the expression √(-20) be simplified?

• i√4

• i√20

• 2i√5

• 4i√5

What happens to the negative sign under a radical when simplifying an imaginary number?

• It becomes positive.

• It manifests as an 'i' outside the radical.

• It is ignored.

• It remains under the radical.