Imaginary Numbers

Open Ended

Explain why a calculator cannot give an answer when you try to find the square root of -9.

Multiple Select

Which of the following statements about imaginary numbers are true?

• Imaginary numbers allow negative numbers to have square roots.

• Imaginary numbers use the unit i.

• Imaginary numbers are the same as real numbers.

• Imaginary numbers were invented to solve equations with no real solutions.

Fill in the Blanks

The unit used to represent imaginary numbers is

Multiple Choice

Which of the following is a pure imaginary number?

• 3i

• 5

• 2 + 4i

• -7

Multiple Choice

Which graph represents a quadratic function with two complex roots?

• The graph that crosses the x-axis twice.

• The graph that touches the x-axis once.

• The graph that does not touch the x-axis at all.

• The graph that is a straight line.

Multiple Select

Which of the following statements about the powers of i are correct?

• i^2= -1

• i^4 = 1

• i^3 = i

• i^1 = i

Multiple Choice

What is the simplified form of i²⁰⁰⁶ ?

• -1

• i

• -i

• 1

Multiple Choice

What is the value of i³ ?

• -i

• i

• -1

• 1

Drag and Drop

Select all correct answers for $$\sqrt[]{-7}$$ =​

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Drag these tiles and drop them in the correct blank above

Fill in the Blanks

The $-\ \sqrt[]{-36}$ can be written as

.

Multiple Choice

$$\sqrt[]{-160}$$

• $$i\ \sqrt[]{160}$$

• $$-4i\ \sqrt[]{10}$$

• $$4i\ \sqrt[]{10}$$

• $$\sqrt[]{160}$$

Open Ended

Describe the process for multiplying two imaginary numbers, such as (2 + i) and (3 + 2i).

Multiple Choice

What is the result of multiplying 2i by the square root of -5?

• 2i√5

• -2√5

• 2√5i

• -2i√5

Multiple Choice

Which of the following expressions results in a real number when simplified?

• √-10 · √-3

• i√-3 · √2

• 3√-4 · i

• -3√-7 · √-7

Fill in the Blanks

3i • 2i =

Open Ended

How confident do you feel about performing operations with imaginary and complex numbers after today's lesson? What would you like to review or learn more about?