Introduction: Begin the lesson by asking students if they have ever heard of complex numbers. Explain that complex numbers are a type of number that includes both real and imaginary parts. Tell them that they will be learning about complex numbers and how to perform operations with them.

Lesson Outline: 1. Define complex numbers and explain the difference between real and imaginary numbers. 2. Introduce the complex plane and how to plot complex numbers on it. 3. Teach students how to perform basic operations with complex numbers, including addition, subtraction, multiplication, and division. 4. Introduce the concept of complex conjugates and how they are used in division. 5. Teach students how to find the modulus and argument of a complex number. 6. Introduce De Moivre’s theorem and how it can be used to find powers and roots of complex numbers.

Questioning: 1. What is a complex number? 2. What is the difference between a real and imaginary number? 3. How do you plot a complex number on the complex plane? 4. How do you perform addition, subtraction, multiplication, and division with complex numbers? 5. What is a complex conjugate and how is it used in division? 6. How do you find the modulus and argument of a complex number? 7. What is De Moivre’s theorem and how is it used to find powers and roots of complex numbers?

Assessment: 1. Have students complete a worksheet on complex numbers. 2. Give students a quiz on the material covered in the lesson. 3. Have students create their own complex numbers and plot them on the complex plane.

Differentiation: 1. Provide extra support for struggling students by giving them additional practice problems. 2. Challenge advanced students by introducing more complex operations with complex numbers. 3. Use visual aids and manipulatives to help students understand the concept of complex numbers.

Plenary: End the lesson by reviewing the material covered and asking students to share one thing they learned about complex numbers. Encourage students to ask any remaining questions they may have.

Resources: 1. Video: Introduction to Complex Numbers 2. Worksheet: Complex Numbers Worksheet 3. Video: Complex Numbers Operations 4. Video: Modulus and Argument of a Complex Number