The Complex Plane

​Introducing the Number i

​

​Learning Goal

• ​Let’s meet i.

​Learning Target

• I can use i to solve equations.​

Introducing the Number i/ Complex Numbers

Vocabulary​

​real number

• ​A number on the number line.

​imaginary number

• A number on the imaginary number line. It can be written as bi, where b is a real number and i² = -1.

​complex number

• ​A number in the complex plane. It can be written as a + bi, where a and b are real numbers and i² = -1.

Open Ended

What is the value of the following expression: $$\left(2\sqrt[]{3}\right)^2$$  

Open Ended

What is the value of the following expression: $$\left(\frac{1}{2}\sqrt[]{3}\right)^2$$  

Open Ended

What is the value of the following expression: $$\left(2\sqrt[]{-1}\right)^2$$  

Open Ended

What is the value of the following expression: $$\left(\frac{1}{2}\sqrt[]{-1}\right)^2$$  

​It is i

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

Simplify:  $$\sqrt[]{225}$$  

• 15, -15

• 20, -20

• 25,- 25

• 30, -30

Subject | Subject

​What are imaginary numbers?

Draw

Simplifying Imaginary Numbers

Multiple Choice

Your Turn!

$$\sqrt[]{-9}$$  

• ±3

• ±3i 

• ±9i

• ±9 

Multiple Choice

Simplify

• $$\pm6$$  

• $$\pm6i$$  

• $$\pm\sqrt[]{6i}$$  

• $$\pm\sqrt[]{6}$$  

Multiple Choice

Solve x² + 81 = 0

• $$\pm\sqrt[]{9i}$$  

• $$\pm9$$  

• $$\pm9i$$  

• $$\pm3i$$  

Draw

Find the solutions to these equations, then plot the solutions to each equation on the imaginary or real number line.

Multiple Choice

What letter usually represent imaginary number?

• a

• i

• j

• x

Multiple Choice

$$\sqrt[]{-1}$$  

• -1

• i

• 1

• -i

Open Ended

Write this imaginary numbers using the number i.

$$-\sqrt[]{-100}$$  

Open Ended

Write this imaginary numbers using the number i.

$$-\sqrt[]{-17}$$  

Open Ended

How do you think you would solve this?

$$i^{15}$$  

Multiple Choice

Your turn! $$i^{22}$$  

• $$\sqrt[]{-1}$$  

• $$-1$$  

• $$-i$$  

• $$1$$  

Multiple Choice

Evaluate $$i^{79}$$  

• $$i$$  

• $$1$$  

• $$-1$$  

• $$-i$$  

Multiple Choice

$$i^7$$  

• $$i$$  

• $$-i$$  

• $$1$$  

• $$-1$$  

​Some text here about the topic of discussion.

​Complex Numbers

​

​What would happen if we tried to add a real number to an imaginary number? How could we represent 5 + i visually?

Open Ended

When we add a real number and an imaginary number, we get a complex number. The diagram shows where 2 + i is in the complex number plane. What complex number is represented by point A?

Draw

Plot these complex numbers in the complex number plane and label them

-2 - i

-6 + 3i

5 + 4i

1 - 3i